// Numbas version: exam_results_page_options
{"duration": 0, "extensions": [], "resources": [], "percentPass": 0, "metadata": {"description": "<p>Practice questions on these topics.</p>", "licence": "Creative Commons Attribution 4.0 International", "notes": ""}, "shuffleQuestions": false, "questions": [{"tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "", "licence": "None specified", "notes": ""}, "statement": "<p>Choose the correct logical expression&nbsp;&nbsp;for the following English sentences.</p>", "parts": [{"prompt": "<p>Let $p$ and $q$ denote respectively the propositions '{choices[0][0]}'&nbsp;and '{choices[0][1]}'.</p>", "layout": {"expression": "", "type": "all"}, "choices": ["<p>{choices[0][2][0]}</p>", "<p>{choices[0][3][0]}</p>", "<p>{choices[0][4][0]}</p>", "<p>{choices[0][5][0]}</p>"], "shuffleChoices": true, "answers": ["<p>{logicl[0][0]}</p>", "<p>{logicl[0][1]}</p>", "<p>{logicl[0][2]}</p>", "<p>{logicl[0][3]}</p>", "<p>{logicl[0][4]}</p>", "<p>{logicl[0][5]}</p>", "<p>{logicl[0][6]}</p>", "<p>{logicl[0][7]}</p>", "<p>{logicl[0][8]}</p>"], "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0]], "warningType": "none", "variableReplacementStrategy": "originalfirst", "shuffleAnswers": true, "minAnswers": 0, "showCorrectAnswer": true, "variableReplacements": [], "displayType": "radiogroup", "type": "m_n_x", "minMarks": 0, "scripts": {}, "maxMarks": 0, "marks": 0, "maxAnswers": 0}, {"prompt": "<p>Let $p$ and $q$ denote respectively the propositions '{choices[1][0]}'&nbsp;and '{choices[1][1]}'.</p>", "layout": {"expression": "", "type": "all"}, "choices": ["<p>{choices[1][2][0]}</p>", "<p>{choices[1][3][0]}</p>", "<p>{choices[1][4][0]}</p>", "<p>{choices[1][5][0]}</p>"], "shuffleChoices": true, "answers": ["<p>{logicl[1][0]}</p>", "<p>{logicl[1][1]}</p>", "<p>{logicl[1][2]}</p>", "<p>{logicl[1][3]}</p>", "<p>{logicl[1][4]}</p>", "<p>{logicl[1][5]}</p>", "<p>{logicl[1][6]}</p>", "<p>{logicl[1][7]}</p>", "<p>{logicl[1][8]}</p>"], "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0]], "warningType": "none", "variableReplacementStrategy": "originalfirst", "shuffleAnswers": true, "minAnswers": 0, "showCorrectAnswer": true, "variableReplacements": [], "displayType": "radiogroup", "type": "m_n_x", "minMarks": 0, "scripts": {}, "maxMarks": 0, "marks": 0, "maxAnswers": 0}, {"prompt": "<p>Let $p$ and $q$ denote respectively the propositions '{choices[2][0]}'&nbsp;and '{choices[2][1]}'.</p>", "layout": {"expression": "", "type": "all"}, "choices": ["<p>{choices[2][2][0]}</p>", "<p>{choices[2][3][0]}</p>", "<p>{choices[2][4][0]}</p>", "<p>{choices[2][5][0]}</p>"], "shuffleChoices": true, "answers": ["<p>{logicl[2][0]}</p>", "<p>{logicl[2][1]}</p>", "<p>{logicl[2][2]}</p>", "<p>{logicl[2][3]}</p>", "<p>{logicl[2][4]}</p>", "<p>{logicl[2][5]}</p>", "<p>{logicl[2][6]}</p>", "<p>{logicl[2][7]}</p>", "<p>{logicl[2][8]}</p>"], "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0]], "warningType": "none", "variableReplacementStrategy": "originalfirst", "shuffleAnswers": true, "minAnswers": 0, "showCorrectAnswer": true, "variableReplacements": [], "displayType": "radiogroup", "type": "m_n_x", "minMarks": 0, "scripts": {}, "maxMarks": 0, "marks": 0, "maxAnswers": 0}], "rulesets": {}, "variables": {"choices": {"definition": "shuffle(all_exp)[0..3]", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "choices"}, "all_exp": {"definition": "[\n  [\n  'It is snowing',\n  'I will go skiing',\n  ['It is not snowing and I will go skiing.',2],\n  ['It will snow if I don\\'t go skiing.',8],\n  ['I will go skiing if it is snowing.',4],\n  ['It is snowing and either I will  not go skiing or it is snowing.',6]\n  ],\n  [\n  'I am working at my studies', \n  'I am in the library',\n  ['I am working at my studies in the library.',1],\n  ['If I am in the library then I am working at my studies.',7],\n  ['If I am working at my studies then I am not in the library.',0],\n  ['Either I am in the library; or I am working at my studies and I am not working at my studies.',10]\n  ],\n  [\n  'It is sunny',\n  'I will carry an umbrella',\n    ['If it is not sunny then I will carry an umbrella.',8],\n    ['It\\'s not sunny and I will carry an umbrella; or it\\'s not sunny.',9],\n    ['I will not carry and umbrella and it is either sunny or it is not.',11],\n    ['If I carry an umbrella then the day always turns out to be sunny!',7]\n  ],\n   [\n  'I am in Omsk',\n  'I am in Siberia',\n  ['I am not in Siberia and  I am not in Omsk.',5],\n  ['It\\'s not true that if I am in Omsk then I am in Siberia.',3],\n  ['If I am  in Omsk then I am in Siberia and  if I am Siberia then I am in Omsk.',12],\n  ['Either I am in Siberia and I am not in Omsk; or I am in Omsk and I am in not Siberia.',13]\n  ]\n  ]", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "all_exp"}, "logic_exp": {"definition": "['$\\\\neg p \\\\lor \\\\neg q$', \n  '$p \\\\land q$', \n  '$\\\\neg p \\\\land q$',\n  '$p \\\\land \\\\neg q$',\n  '$p \\\\to q$',\n  '$\\\\neg p \\\\land \\\\neg q$',\n  '$(p \\\\lor \\\\neg q) \\\\land p$',\n  '$q \\\\to p$',\n  '$\\\\neg p \\\\to q$'\n  ]", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "logic_exp"}, "all_logic": {"definition": "['$\\\\neg p \\\\lor \\\\neg q$', \n  '$p \\\\land q$', \n  '$\\\\neg p \\\\land q$',\n  '$p \\\\land \\\\neg q$',\n  '$p \\\\to q$',\n  '$\\\\neg p \\\\land \\\\neg q$',\n  '$(p \\\\lor \\\\neg q) \\\\land p$',\n  '$q \\\\to p$',\n  '$\\\\neg p \\\\to q$',\n  '$(\\\\neg p \\\\land q) \\\\lor \\\\neg p$',\n  '$q \\\\lor  (p \\\\land \\\\neg p)$',\n  '$\\\\neg q \\\\land (p \\\\lor \\\\neg p)$',\n  '$p \\\\leftrightarrow q$',\n  '$(p \\\\land \\\\neg q) \\\\lor (\\\\neg p \\\\land q)$'\n  ]", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "all_logic"}, "correctl": {"definition": "map(map(choices[y][x][1],x,2..5),y,0..2)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "correctl"}, "logicl": {"definition": "map(map(all_logic[gloryl[y][x]],x,0..8),y,0..2)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "logicl"}, "faithl": {"definition": "map(shuffle(hopel[x])[0..5],x,0..2)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "faithl"}, "hopel": {"definition": "map(list(set(0,1,2,3,4,5,6,7,8,9,10,11,12,13)-set(correctl[x])),x,0..2)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "hopel"}, "gloryl": {"definition": "map(correctl[x]+list(set(faithl[x])),x,0..2)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "gloryl"}}, "advice": "", "preamble": {"js": "", "css": ""}, "variable_groups": [{"variables": [], "name": "Unnamed group"}], "functions": {}, "ungrouped_variables": ["choices", "logic_exp", "correctl", "hopel", "gloryl", "all_logic", "faithl", "all_exp", "logicl"], "name": "Propositions - old - MAS1701-ajd"}, {"tags": ["logic", "quantifiers", "statements"], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "<p>English sentences which are propositions are given and for each the appropriate proposition&nbsp;&nbsp;involving quantifiers is to be chosen.&nbsp;</p>", "licence": "None specified", "notes": ""}, "statement": "<p>In a seminar group, for group members $m$ and $n$, we let $P(m,n)$ to be the predicate&nbsp;<strong><em>m knows the name of n&nbsp;</em></strong>.</p>\n<p>For each English sentence choose the corresponding proposition involving quantifiers.</p>\n<p>Note that you will lose one mark for every incorrect choice. However, the minimum mark is $0$.</p>", "parts": [{"prompt": "<p>The numbers heading the columns refer to the following:</p>\n<p><strong>1</strong>. &nbsp;{all[select[0]][1]}</p>\n<p><strong>2</strong>. &nbsp;{all[select[1]][1]}</p>\n<p><strong>3</strong>. &nbsp;{all[select[2]][1]}</p>\n<p><strong>4. &nbsp;</strong>{all[select[3]][1]}</p>", "layout": {"expression": "", "type": "all"}, "choices": ["{all[select[0]][0]}", "{all[select[1]][0]}", "{all[select[2]][0]}", "{all[select[3]][0]}"], "shuffleChoices": true, "answers": ["<p><strong>1</strong></p>", "<p><strong>2</strong></p>", "<p><strong>3</strong></p>", "<p><strong>4</strong></p>"], "matrix": "marks", "warningType": "warn", "variableReplacementStrategy": "originalfirst", "shuffleAnswers": false, "minAnswers": "4", "showCorrectAnswer": true, "variableReplacements": [], "displayType": "radiogroup", "type": "m_n_x", "minMarks": 0, "scripts": {}, "maxMarks": 0, "marks": 0, "maxAnswers": "4"}, {"prompt": "<p>The numbers heading the columns refer to the following:</p>\n<p><strong>1</strong>. &nbsp;{all[select1[0]][1]}</p>\n<p><strong>2</strong>. &nbsp;{all[select1[1]][1]}</p>\n<p><strong>3</strong>. &nbsp;{all[select1[2]][1]}</p>\n<p><strong>4. &nbsp;</strong>{all[select1[3]][1]}</p>", "layout": {"expression": "", "type": "all"}, "choices": ["{all[select1[0]][0]}", "{all[select1[1]][0]}", "{all[select1[2]][0]}", "{all[select1[3]][0]}"], "shuffleChoices": true, "answers": ["<p><strong>1</strong></p>", "<p><strong>2</strong></p>", "<p><strong>3</strong></p>", "<p><strong>4</strong></p>"], "matrix": "marks", "warningType": "warn", "variableReplacementStrategy": "originalfirst", "shuffleAnswers": false, "minAnswers": "4", "showCorrectAnswer": true, "variableReplacements": [], "displayType": "radiogroup", "type": "m_n_x", "minMarks": 0, "scripts": {}, "maxMarks": 0, "marks": 0, "maxAnswers": "4"}, {"prompt": "<p>The numbers heading the columns refer to the following:</p>\n<p><strong>1</strong>. &nbsp;{all[select2[0]][1]}</p>\n<p><strong>2</strong>. &nbsp;{all[select2[1]][1]}</p>\n<p><strong>3</strong>. &nbsp;{all[select2[2]][1]}</p>\n<p><strong>4. &nbsp;</strong>{all[select2[3]][1]}</p>", "layout": {"expression": "", "type": "all"}, "choices": ["{all[select2[0]][0]}", "{all[select2[1]][0]}", "{all[select2[2]][0]}", "{all[select2[3]][0]}"], "shuffleChoices": true, "answers": ["<p><strong>1</strong></p>", "<p><strong>2</strong></p>", "<p><strong>3</strong></p>", "<p><strong>4</strong></p>"], "matrix": "marks", "warningType": "warn", "variableReplacementStrategy": "originalfirst", "shuffleAnswers": false, "minAnswers": "4", "showCorrectAnswer": true, "variableReplacements": [], "displayType": "radiogroup", "type": "m_n_x", "minMarks": 0, "scripts": {}, "maxMarks": 0, "marks": 0, "maxAnswers": "4"}], "rulesets": {}, "variables": {"select": {"definition": "shuffle(list(0..length(all)-1))[0..4]", "description": "", "group": "Part 0", "templateType": "anything", "name": "select"}, "marks": {"definition": "matrix(list(2*id(4)-matrix(repeat(repeat(1,4),4))))", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "marks"}, "all": {"definition": "[['There is someone not known to the rest.',\n    '$\\\\exists m \\\\forall n (\\\\neg P(n,m))$'],\n  ['Every group member doesn\\'t know the name of at least one other.',\n    '$\\\\forall m \\\\exists n (\\\\neg P(m,n))$'],\n  ['Nobody knows the name of anybody else.',\n    '$\\\\forall m \\\\forall n (\\\\neg P(m,n))$'],\n  ['There is a pair of group members who do not know each other\\'s name.',\n    '$\\\\exists m \\\\exists n (\\\\neg P(m,n) \\\\land \\\\neg P(n,m)$'],\n  ['There is someone who knows everyone\\'s name.',\n    '$\\\\exists m \\\\forall n (P(m,n))$'],\n  ['There is at least one person who knows the name of somebody else.',\n    '$\\\\exists m \\\\exists n (P(n,m))$'],\n  ['There is someone who doesn\\'t know the name of at least one other group member.',\n    '$\\\\exists m \\\\exists n (\\\\neg P(n,m))$'],\n  ['Someone\\'s name is known to everyone else.',\n    '$\\\\exists m \\\\forall n ( P(n,m))$'],\n  ['There is at least one person who does not know the name of anybody else.',\n    '$\\\\exists m \\\\forall n (\\\\neg P(m,n))$'],\n  ['Everybody knows at least one other person\\'s name.',\n    '$\\\\forall m \\\\exists n (P(m,n))$'],\n  ['Any member of the group has at least one person who doesn\\'t know their name.',\n    '$\\\\forall n \\\\exists m (\\\\neg P(m,n))$'],\n  ['There are at least two people who know each other\\'s name.',\n    '$\\\\exists n \\\\exists m (P(n,m) \\\\land P(m,n))$']\n  \n  ]", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "all"}, "select1": {"definition": "list(set(0..length(all)-1)-set(select))[0..4]", "description": "", "group": "Part 1", "templateType": "anything", "name": "select1"}, "select2": {"definition": "list(set(0..length(all)-1)-(set(select) or set(select1)))", "description": "", "group": "Part 2", "templateType": "anything", "name": "select2"}}, "advice": "", "preamble": {"js": "", "css": ""}, "variable_groups": [{"variables": ["select"], "name": "Part 0"}, {"variables": ["select1"], "name": "Part 1"}, {"variables": ["select2"], "name": "Part 2"}], "functions": {}, "ungrouped_variables": ["all", "marks"], "name": "Quantifiers 2-MAS1701"}, {"tags": ["exists", "for all", "logic", "logical expressions", "negation of logical expressions", "negation of quantifiers", "predicates", "quantifiers"], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "<p>Given&nbsp;two propositions&nbsp;in mathematics using quantifiers, choose the corresponding negation of the proposition. For example, the negation of: $\\displaystyle \\exists a \\in \\mathbb{R^+},\\;\\exists b \\in \\mathbb{N},\\;\\exists c \\in \\mathbb{N}\\;\\left[(c \\lt b+1) \\land \\left(\\frac{1}{2^n} \\geq 3a\\right)\\right]$</p>", "licence": "None specified", "notes": ""}, "statement": "<p></p>\n<p></p>\n<p></p>", "parts": [{"displayColumns": "1", "prompt": "<p>Choose the negation of&nbsp;&nbsp; \\[\\var{latex(Prop_const[0][0])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][0])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][0])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(Prop_const[3][0])})\\, \\var{latex(Prop_const[5][0])}\\, \\left(\\var{latex(Prop_const[4][0])}\\right)\\right]\\]</p>\n<p>from the list below</p>", "choices": ["<p></p>\n<p>$\\displaystyle &nbsp;\\var{latex(Prop_const[0][1])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][1])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][1])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(Prop_const[3][0])})\\, \\var{latex(Prop_const[5][1])}\\, \\left(\\var{latex(Prop_const[4][1])}\\right)\\right]$</p>", "<p>$\\displaystyle &nbsp;\\var{latex(Prop_const[0][wrong_flags[0][0]])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][wrong_flags[0][1]])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][wrong_flags[0][2]])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(Prop_const[3][0])})\\, \\var{latex(Prop_const[5][wrong_flags[0][3]])}\\, \\left(\\var{latex(Prop_const[4][wrong_flags[0][4]])}\\right)\\right]$</p>", "<p>$\\displaystyle \\var{latex(Prop_const[0][wrong_flags[1][0]])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][wrong_flags[1][1]])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][wrong_flags[1][2]])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(Prop_const[3][0])})\\, \\var{latex(Prop_const[5][wrong_flags[1][3]])}\\, \\left(\\var{latex(Prop_const[4][wrong_flags[1][4]])}\\right)\\right]$</p>", "<p>&nbsp;$\\displaystyle &nbsp;\\var{latex(Prop_const[0][wrong_flags[2][0]])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][wrong_flags[2][1]])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][wrong_flags[2][2]])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(Prop_const[3][0])})\\, \\var{latex(Prop_const[5][wrong_flags[2][3]])}\\, \\left(\\var{latex(Prop_const[4][wrong_flags[2][4]])}\\right)\\right]$</p>"], "shuffleChoices": true, "variableReplacementStrategy": "originalfirst", "marks": 0, "matrix": ["4", 0, 0, 0], "variableReplacements": [], "displayType": "radiogroup", "type": "1_n_2", "minMarks": 0, "scripts": {}, "distractors": ["", "", "", ""], "maxMarks": "4", "showCorrectAnswer": true}, {"displayColumns": "1", "prompt": "<p>Choose the negation of&nbsp;</p>\n<p>\\[\\var{latex(Prop_const[0][1])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][0])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][1])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(prop2[0][0])})\\, \\var{latex(Prop_const[5][1])}\\, \\left(\\var{latex(prop2[1][1])}\\right)\\right]\\]</p>\n<p>from the list below</p>", "choices": ["<p>$\\displaystyle \\var{latex(Prop_const[0][0])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][1])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][0])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(prop2[0][0])})\\, \\var{latex(Prop_const[5][0])}\\, \\left(\\var{latex(prop2[1][0])}\\right)\\right]$</p>", "<p>$\\displaystyle &nbsp;\\var{latex(Prop_const[0][1-wrong_flags[1][0]])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][wrong_flags[1][1]])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][1-wrong_flags[1][2]])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(prop2[0][0])})\\, \\var{latex(Prop_const[5][1-wrong_flags[1][3]])}\\, \\left(\\var{latex(prop2[1][1-wrong_flags[1][4]])}\\right)\\right]$</p>\n<p></p>", "<p>$\\displaystyle &nbsp;\\var{latex(Prop_const[0][1-wrong_flags[2][0]])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][wrong_flags[2][1]])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][1-wrong_flags[2][2]])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(prop2[0][0])})\\, \\var{latex(Prop_const[5][1-wrong_flags[2][3]])}\\, \\left(\\var{latex(prop2[1][1-wrong_flags[2][4]])}\\right)\\right]$</p>\n<p></p>", "<p>$\\displaystyle &nbsp;\\var{latex(Prop_const[0][1-wrong_flags[3][0]])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][wrong_flags[3][1]])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][1-wrong_flags[3][2]])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(prop2[0][0])})\\, \\var{latex(Prop_const[5][1-wrong_flags[3][3]])}\\, \\left(\\var{latex(prop2[1][1-wrong_flags[3][4]])}\\right)\\right]$</p>"], "shuffleChoices": true, "variableReplacementStrategy": "originalfirst", "marks": 0, "matrix": ["4", 0, 0, 0], "variableReplacements": [], "displayType": "radiogroup", "type": "1_n_2", "minMarks": 0, "scripts": {}, "distractors": ["", "", "", ""], "maxMarks": "4", "showCorrectAnswer": true}], "rulesets": {}, "variables": {"wrong_flags": {"definition": "shuffle([shuffle([0,1,1,1,1]),shuffle([0,0,1,1,1]),shuffle([0,0,0,1,1]),shuffle([0,0,0,0,1])])[0..4]", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "wrong_flags"}, "Bchoice": {"definition": "[\n[\"|(-1)\\^c| < a\",\"|(-1)\\^c| \\\\ge a\"],\n[\"\\\\left|\\\\sqrt\\{\\\\left(1-\\\\frac\\{1\\}\\{c\\}\\\\right)\\}-1\\\\right| < a\",\"a \\\\leq \\\\left| \\\\sqrt\\{\\\\left(1-\\\\frac\\{1\\}\\{c\\}\\\\right)\\}-1 \\\\right|\"],\n[\"\\\\frac\\{1\\}\\{2\\^c\\} < 3a\",\"\\\\frac\\{1\\}\\{2\\^c\\} \\\\ge 3a\"],\n[\"\\\\frac\\{c\\^2-2\\}\\{2c+3\\} > 3a+6\",\"\\\\frac\\{c\\^2-2\\}\\{2c+3\\} \\\\le 3a+6\"],\n[\"\\\\left|\\\\frac\\{1\\}\\{c\\^3\\}\\\\right| < a\",\"\\\\left|\\\\frac\\{1\\}\\{c\\^3\\}\\\\right| \\\\ge a\"],\n[\"\\\\frac\\{c\\^2+6\\}\\{2c\\^2+1\\} < a\",\"\\\\frac\\{c\\^2+6\\}\\{2c\\^2+1\\} \\\\ge a\"]\n]\n", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "Bchoice"}, "Prop_const": {"definition": "[random(Qchoice),random(Qchoice),random(Qchoice),random(Achoice),random(Bchoice),random(Cchoice)]", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "Prop_const"}, "prop2": {"definition": "[random(Achoice),random(Bchoice)]", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "prop2"}, "Achoice": {"definition": "[\n[\"c \\\\ge b\"],\n[\"c < b\"],\n[\"c = b\"],\n[\"c \\\\neq b\"],\n[\"2c\\\\le b\"],\n[\"c\\\\ge b+1\"],\n[\"c < b+1\"],\n[\"2c > b\"]\n]", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "Achoice"}, "Qchoice": {"definition": "[\n  [\"\\\\forall\",\"\\\\exists\"],\n  [\"\\\\exists\",\"\\\\forall\"]\n]", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "Qchoice"}, "Cchoice": {"definition": "[[\"\\\\rightarrow\",\"\\\\land\"],\n  [\"\\\\land\",\"\\\\rightarrow\"]\n  ]", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "Cchoice"}}, "advice": "", "preamble": {"js": "", "css": ""}, "variable_groups": [], "functions": {}, "ungrouped_variables": ["Prop_const", "Cchoice", "Achoice", "Qchoice", "Bchoice", "wrong_flags", "prop2"], "name": "Quantifiers 4-MAS1701-AJD"}, {"tags": ["logic", "quantifiers", "statements"], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "<p>English sentences are given and for each the appropriate proposition&nbsp;involving quantifiers is to be chosen. Also choose whether the propositions are true or false.</p>", "licence": "None specified", "notes": ""}, "statement": "<p>Choose the appropriate proposition&nbsp;&nbsp;for the following English sentences. Also choose whether they are true or false.</p>\n<p>You must make $2$ choices in each row, one of which is to determine whether the proposition&nbsp;&nbsp;is true or false.</p>\n<p>Note also that every wrong answer takes away one from your score. However, your minimum score is $0$.</p>", "parts": [{"choices": ["{all[select[0]][0]}", "{all[select[1]][0]}", "{all[select[2]][0]}"], "shuffleChoices": true, "answers": ["{all[select[0]][1]}", "{all[select[1]][1]}", "{all[select[2]][1]}", "True", "False"], "matrix": "marking_matrix", "warningType": "warn", "layout": {"expression": "", "type": "all"}, "shuffleAnswers": false, "minAnswers": "6", "showCorrectAnswer": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "m_n_x", "minMarks": 0, "displayType": "checkbox", "scripts": {}, "maxMarks": 0, "marks": 0, "maxAnswers": "6"}, {"choices": ["{all[select1[0]][0]}", "{all[select1[1]][0]}", "{all[select1[2]][0]}"], "shuffleChoices": true, "answers": ["{all[select1[0]][1]}", "{all[select1[1]][1]}", "{all[select1[2]][1]}", "True", "False"], "matrix": "marking_matrix1", "warningType": "warn", "layout": {"expression": "", "type": "all"}, "shuffleAnswers": false, "minAnswers": "6", "showCorrectAnswer": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "m_n_x", "minMarks": 0, "displayType": "checkbox", "scripts": {}, "maxMarks": 0, "marks": 0, "maxAnswers": "6"}, {"choices": ["{all[select2[0]][0]}", "{all[select2[1]][0]}", "{all[select2[2]][0]}"], "shuffleChoices": true, "answers": ["{all[select2[0]][1]}", "{all[select2[1]][1]}", "{all[select2[2]][1]}", "True", "False"], "matrix": "marking_matrix2", "warningType": "warn", "layout": {"expression": "", "type": "all"}, "shuffleAnswers": false, "minAnswers": "6", "showCorrectAnswer": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "m_n_x", "minMarks": 0, "displayType": "checkbox", "scripts": {}, "maxMarks": 0, "marks": 0, "maxAnswers": "6"}], "rulesets": {}, "variables": {"all": {"definition": "[['The square of any real number is greater than $0$.',\n    '$\\\\forall x \\\\in \\\\mathbb{R}\\\\;(x^2\\\\gt 0).$',-1],\n  ['Given a real number then some integral power is not negative.',\n    '$\\\\forall x \\\\in \\\\mathbb{R} \\\\;\\\\exists n \\\\in \\\\mathbb{N}\\\\;(x^n\\\\geq 0).$',1],\n  ['A subset of the natural numbers is a subset of the reals.',\n    '$\\\\forall X \\\\subseteq \\\\mathbb{N}\\\\;(X\\\\subseteq \\\\mathbb{R}).$',1],\n  ['For every natural number $n$ there is a subset of $\\\\mathbb{N}$ with less than $n$ members.',\n    '$\\\\forall n \\\\in \\\\mathbb{N}\\\\;\\\\exists X \\\\subseteq \\\\mathbb{N}\\\\;(|X|\\\\lt n).$',1],\n  ['All subsets of the natural numbers have less than a fixed number of elements.',\n    '$\\\\exists n \\\\in \\\\mathbb{N}\\\\; \\\\forall X \\\\subseteq \\\\mathbb{N}\\\\;(|X|\\\\lt n).$',-1],\n  ['All subsets of the natural numbers are finite.',\n    '$\\\\forall X \\\\subseteq \\\\mathbb{N}\\\\;\\\\exists n \\\\in \\\\mathbb{Z}\\\\;(|X|=n).$',-1],\n  ['Given an integer $n$, there is a subset of the natural numbers with $n$ elements.',\n    '$\\\\forall n \\\\in \\\\mathbb{Z}\\\\;\\\\exists X \\\\subseteq \\\\mathbb{N}\\\\;(|X|=n).$',-1],\n  ['Given an integer, then adding $5$ to it gives another integer.',\n    '$\\\\forall n \\\\in \\\\mathbb{Z}\\\\; \\\\exists m \\\\in \\\\mathbb{Z}\\\\; (m=n+5).$',1],\n  ['There is an integer $t$ such that adding $5$ to any integer gives $t$.',\n    '$\\\\exists m \\\\in \\\\mathbb{Z}\\\\; \\\\forall n \\\\in \\\\mathbb{Z}\\\\; (m=n+5).$',-1]\n  ]", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "all"}, "marking_matrix2": {"definition": "map(list(neg_marks[x])+[all[select2[x]][2]]+[-1*all[select2[x]][2]],x,0..2)", "description": "", "group": "Part 2", "templateType": "anything", "name": "marking_matrix2"}, "select2": {"definition": "list(set(0..length(all)-1)-(set(select) or set(select1)))", "description": "", "group": "Part 2", "templateType": "anything", "name": "select2"}, "select1": {"definition": "list(set(0..length(all)-1)-set(select))[0..3]", "description": "", "group": "Part 1", "templateType": "anything", "name": "select1"}, "neg_marks": {"definition": "2*id(3)+matrix(map(map(-1,x,0..2),y,0..2))", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "neg_marks"}, "select": {"definition": "shuffle(list(0..length(all)-1))[0..3]", "description": "", "group": "Part 0", "templateType": "anything", "name": "select"}, "marking_matrix1": {"definition": "map(list(neg_marks[x])+[all[select1[x]][2]]+[-1*all[select1[x]][2]],x,0..2)", "description": "", "group": "Part 1", "templateType": "anything", "name": "marking_matrix1"}, "marking_matrix": {"definition": "map(list(neg_marks[x])+[all[select[x]][2]]+[-1*all[select[x]][2]],x,0..2)", "description": "", "group": "Part 0", "templateType": "anything", "name": "marking_matrix"}}, "advice": "", "preamble": {"js": "", "css": ""}, "variable_groups": [{"variables": ["marking_matrix", "select"], "name": "Part 0"}, {"variables": ["select1", "marking_matrix1"], "name": "Part 1"}, {"variables": ["select2", "marking_matrix2"], "name": "Part 2"}], "functions": {}, "ungrouped_variables": ["all", "neg_marks"], "name": "Quantifiers1-MAS1701"}, {"tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "", "licence": "None specified", "notes": ""}, "statement": "<p>Write the following sets in enumerated form.</p>\n<p>Note that you enter an enumerated set such as $\\{35,67,99\\}$ as <code>set(35,67,99)</code>.</p>\n<p></p>", "parts": [{"prompt": "<p>a) $A=\\{x \\in \\mathbb{N}\\;|\\;\\var{a} \\leq x \\leq \\var{b}\\text{ and } x \\text{ is divisible by }\\var{c}\\}$.</p>\n<p>$A=\\;$[[0]]</p>\n<p>b) $B=\\{x \\in \\mathbb{Z}\\;|\\;\\var{d} \\leq x \\leq \\var{f}\\text{ and } x^2 \\lt \\var{g}\\}$.</p>\n<p>$B=\\;$[[1]]</p>\n<p>c) $C=\\{x \\in \\mathbb{Z}\\;|\\;\\var{d} \\leq x \\leq \\var{f}\\text{ and } x^2 \\gt \\var{g}\\}$.</p>\n<p>$C=\\;$[[2]]</p>\n<p>d) $A \\cap C=\\;$[[3]]</p>\n<p></p>\n<p>Note that you input sets in the form <code>set(a,b,c,..,z)</code> .</p>\n<p>For example <code> set(1,2,3)</code>gives the set $\\{1,2,3\\}$.</p>\n<p>The empty set is input as&nbsp;<code>set()</code>.</p>\n<p>Also some labour saving tips:</p>\n<p>If you want to input all integers between $a$ and $b$ inclusive then instead of writing all the elements you can input this as <code>set(a..b)</code>.</p>\n<p>If you want to input all integers between $a$ and $b$ inclusive in steps of $c$ then this is input as <code>set(a..b#c)</code>. So all odd integers from $-3$ to $28$ are input as&nbsp;<code>set(-3..28#2).</code></p>", "variableReplacements": [], "showCorrectAnswer": true, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "scripts": {}, "gaps": [{"marks": 1, "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{answer_set1}", "vsetrange": [0, 1], "vsetrangepoints": 5, "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "checkvariablenames": false, "scripts": {}, "expectedvariablenames": [], "showpreview": true, "showCorrectAnswer": true}, {"marks": 1, "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{answer_set2}", "vsetrange": [0, 1], "vsetrangepoints": 5, "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "checkvariablenames": false, "scripts": {}, "expectedvariablenames": [], "showpreview": true, "showCorrectAnswer": true}, {"marks": 1, "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{answer_set3}", "vsetrange": [0, 1], "vsetrangepoints": 5, "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "checkvariablenames": false, "scripts": {}, "expectedvariablenames": [], "showpreview": true, "showCorrectAnswer": true}, {"marks": 1, "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{answer_set4}", "vsetrange": [0, 1], "vsetrangepoints": 5, "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "checkvariablenames": false, "scripts": {}, "expectedvariablenames": [], "showpreview": true, "showCorrectAnswer": true}], "marks": 0}], "rulesets": {}, "variables": {"answer_set3": {"definition": "set(d..f) and(set(d-1..-r-1) or set(r+1..f+1))", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "answer_set3"}, "answer_set1": {"definition": "set(mod_set(a,b,c))", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "answer_set1"}, "d": {"definition": "random(-25..-5)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "d"}, "b": {"definition": "a+random(12..30)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}, "g": {"definition": "r^2", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "g"}, "f": {"definition": "random(10..25)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "f"}, "answer_set4": {"definition": "answer_set1 and answer_set3", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "answer_set4"}, "c": {"definition": "random(3..7)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "c"}, "answer_set2": {"definition": "set(-r+1..r-1)and set(d..f)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "answer_set2"}, "a": {"definition": "random(8..20)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}, "r": {"definition": "random(8..15)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "r"}}, "advice": "", "preamble": {"js": "", "css": ""}, "variable_groups": [], "functions": {"mod_set": {"definition": "//returns all integers which are divisible by c betweeen a and b\nvar l=[];\nfor(var i=a;i<b+1;i++) \n{ if (i%c==0){l.push(i);}\n}\nreturn l;\n", "parameters": [["a", "number"], ["b", "number"], ["c", "number"]], "type": "list", "language": "javascript"}}, "ungrouped_variables": ["a", "b", "c", "answer_set1", "d", "f", "g", "answer_set2", "r", "answer_set3", "answer_set4"], "name": "set1 - MAS1701"}, {"tags": [], "variablesTest": {"maxRuns": "200", "condition": "gcd(a2,b2)=1 and gcd(a3,b3)<>1"}, "metadata": {"description": "", "licence": "None specified", "notes": ""}, "statement": "<p>Enumerate each of the following sets.</p>\n<p></p>\n<p>Note that you input sets in the form <code>set(a,b,c,..,z)</code> .</p>\n<p>For example <code> set(1,2,3)</code>gives the set $\\{1,2,3\\}$.</p>\n<p>The empty set is input as&nbsp;<code>set()</code>.</p>\n<p>Also some labour saving tips:</p>\n<p>If you want to input all integers between $a$ and $b$ inclusive then instead of writing all the elements you can input this as <code>set(a..b)</code>.</p>\n<p>If you want to input all integers between $a$ and $b$ inclusive in steps of $c$ then this is input as <code>set(a..b#c)</code>. So all odd integers from $-3$ to $28$ are input as&nbsp;<code>set(-3..28#2).</code></p>", "parts": [{"prompt": "<p>1) $S=\\{y\\;|\\;y \\in \\mathbb{Z}, y=\\var{a}x-\\var{c},\\;x \\in \\mathbb{Z}\\text{ and } |y| \\leq \\var{b}\\}$</p>\n<p>$S\\;$=[[0]]</p>\n<p>2) $S=\\{y\\;|\\;y \\in \\mathbb{N}, y=\\var{a}x-\\var{c},\\;x \\in \\mathbb{Z}\\text{ and } |y| \\leq \\var{b}\\}$</p>\n<p>$S\\;$=[[1]]</p>\n<p>3)&nbsp;$S=\\{x\\:| x \\in \\mathbb{Z}\\text{ and }\\;|\\var{a1}x-\\var{c1}| \\leq \\var{b1}\\}$.</p>\n<p>$S=\\;$[[2]]</p>\n<p>4) $S=\\{x\\:| x \\in \\mathbb{N}\\text{ and }\\;|\\var{a1}x-\\var{c1}| \\leq \\var{b1}\\}$.</p>\n<p>$S=\\;$[[3]]</p>", "variableReplacements": [], "showCorrectAnswer": true, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "scripts": {}, "gaps": [{"marks": 1, "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{ans1}", "vsetrange": [0, 1], "vsetrangepoints": 5, "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "checkvariablenames": false, "scripts": {}, "expectedvariablenames": [], "showpreview": true, "showCorrectAnswer": true}, {"marks": 1, "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{ans2}", "vsetrange": [0, 1], "vsetrangepoints": 5, "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "checkvariablenames": false, "scripts": {}, "expectedvariablenames": [], "showpreview": true, "showCorrectAnswer": true}, {"marks": 1, "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{ans3}", "vsetrange": [0, 1], "vsetrangepoints": 5, "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "checkvariablenames": false, "scripts": {}, "expectedvariablenames": [], "showpreview": true, "showCorrectAnswer": true}, {"marks": 1, "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{ans4}", "vsetrange": [0, 1], "vsetrangepoints": 5, "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "checkvariablenames": false, "scripts": {}, "expectedvariablenames": [], "showpreview": true, "showCorrectAnswer": true}], "marks": 0}, {"prompt": "<p>1) $S=\\{\\var{a2}a+\\var{b2}b\\;|\\;a,\\;b \\in \\mathbb{Z},\\;|\\var{a2}a+\\var{b2}b\\,|\\lt \\var{c2}\\}$.</p>\n<p>$S=\\;$[[0]]</p>\n<p>2) $S=\\{\\var{a3}a+\\var{b3}b\\;|\\;a,\\;b \\in \\mathbb{Z},\\;|\\var{a3}a+\\var{b3}b\\,|\\lt \\var{c3}\\}$.</p>\n<p>$S=\\;$[[1]]</p>\n<p></p>", "variableReplacements": [], "showCorrectAnswer": true, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "scripts": {}, "gaps": [{"marks": 1, "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{set(-c2+1..c2-1)}", "vsetrange": [0, 1], "vsetrangepoints": 5, "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "checkvariablenames": false, "scripts": {}, "expectedvariablenames": [], "showpreview": true, "showCorrectAnswer": true}, {"marks": 1, "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{set(g*ceil((-c3+1)/g)..(c3-1)#g)}", "vsetrange": [0, 1], "vsetrangepoints": 5, "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "checkvariablenames": false, "scripts": {}, "expectedvariablenames": [], "showpreview": true, "showCorrectAnswer": true}], "marks": 0}], "rulesets": {}, "variables": {"a3": {"definition": "random(2..15)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a3"}, "ans3": {"definition": "set(ceil((c1-b1)/a1)..floor((c1+b1)/a1))", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "ans3"}, "ans4": {"definition": "ans3 and set(1..floor((c1+b1)/a1))", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "ans4"}, "a2": {"definition": "random(2..6)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a2"}, "ans2": {"definition": "ans1 and set(1..b)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "ans2"}, "a": {"definition": "random(2..6)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}, "a1": {"definition": "random(2..6 except a)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a1"}, "c2": {"definition": "random(4..10)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "c2"}, "b1": {"definition": "random(6..10 except b)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "b1"}, "c1": {"definition": "random(3..6 except c)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "c1"}, "g": {"definition": "gcd(a3,b3)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "g"}, "c3": {"definition": "random(6..10)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "c3"}, "c": {"definition": "random(3..8)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "c"}, "b": {"definition": "random(2..10)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}, "b3": {"definition": "random(2..12)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "b3"}, "b2": {"definition": "random(2..12)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "b2"}, "ans1": {"definition": "set(a*ceil((c-b)/a)-c..a*floor((c+b)/a)-c#a)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "ans1"}}, "advice": "", "preamble": {"js": "", "css": ""}, "variable_groups": [], "functions": {}, "ungrouped_variables": ["a", "b", "c", "ans1", "ans2", "a1", "b1", "c1", "ans3", "ans4", "a2", "b2", "c2", "a3", "b3", "c3", "g"], "name": "set4-MAS1701"}], "question_groups": [{"questions": [{"name": "Propositions - old-ajd", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "variable_groups": [{"variables": [], "name": "Unnamed group"}], "variables": {"faithl": {"templateType": "anything", "group": "Ungrouped variables", "definition": "map(shuffle(hopel[x])[0..5],x,0..2)", "description": "", "name": "faithl"}, "logicl": {"templateType": "anything", "group": "Ungrouped variables", "definition": "map(map(all_logic[gloryl[y][x]],x,0..8),y,0..2)", "description": "", "name": "logicl"}, "logic_exp": {"templateType": "anything", "group": "Ungrouped variables", "definition": "['$\\\\neg p \\\\lor \\\\neg q$', \n  '$p \\\\land q$', \n  '$\\\\neg p \\\\land q$',\n  '$p \\\\land \\\\neg q$',\n  '$p \\\\to q$',\n  '$\\\\neg p \\\\land \\\\neg q$',\n  '$(p \\\\lor \\\\neg q) \\\\land p$',\n  '$q \\\\to p$',\n  '$\\\\neg p \\\\to q$'\n  ]", "description": "", "name": "logic_exp"}, "choices": {"templateType": "anything", "group": "Ungrouped variables", "definition": "shuffle(all_exp)[0..3]", "description": "", "name": "choices"}, "correctl": {"templateType": "anything", "group": "Ungrouped variables", "definition": "map(map(choices[y][x][1],x,2..5),y,0..2)", "description": "", "name": "correctl"}, "all_logic": {"templateType": "anything", "group": "Ungrouped variables", "definition": "['$\\\\neg p \\\\lor \\\\neg q$', \n  '$p \\\\land q$', \n  '$\\\\neg p \\\\land q$',\n  '$p \\\\land \\\\neg q$',\n  '$p \\\\to q$',\n  '$\\\\neg p \\\\land \\\\neg q$',\n  '$(p \\\\lor \\\\neg q) \\\\land p$',\n  '$q \\\\to p$',\n  '$\\\\neg p \\\\to q$',\n  '$(\\\\neg p \\\\land q) \\\\lor \\\\neg p$',\n  '$q \\\\lor  (p \\\\land \\\\neg p)$',\n  '$\\\\neg q \\\\land (p \\\\lor \\\\neg p)$',\n  '$p \\\\leftrightarrow q$',\n  '$(p \\\\land \\\\neg q) \\\\lor (\\\\neg p \\\\land q)$'\n  ]", "description": "", "name": "all_logic"}, "hopel": {"templateType": "anything", "group": "Ungrouped variables", "definition": "map(list(set(0,1,2,3,4,5,6,7,8,9,10,11,12,13)-set(correctl[x])),x,0..2)", "description": "", "name": "hopel"}, "gloryl": {"templateType": "anything", "group": "Ungrouped variables", "definition": "map(correctl[x]+list(set(faithl[x])),x,0..2)", "description": "", "name": "gloryl"}, "all_exp": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[\n  [\n  'It is snowing',\n  'I will go skiing',\n  ['It is not snowing and I will go skiing.',2],\n  ['It will snow if I don\\'t go skiing.',8],\n  ['I will go skiing if it is snowing.',4],\n  ['It is snowing and either I will  not go skiing or it is snowing.',6]\n  ],\n  [\n  'I am working at my studies', \n  'I am in the library',\n  ['I am working at my studies in the library.',1],\n  ['If I am in the library then I am working at my studies.',7],\n  ['If I am working at my studies then I am not in the library.',0],\n  ['Either I am in the library; or I am working at my studies and I am not working at my studies.',10]\n  ],\n  [\n  'It is sunny',\n  'I will carry an umbrella',\n    ['If it is not sunny then I will carry an umbrella.',8],\n    ['It\\'s not sunny and I will carry an umbrella; or it\\'s not sunny.',9],\n    ['I will not carry and umbrella and it is either sunny or it is not.',11],\n    ['If I carry an umbrella then the day always turns out to be sunny!',7]\n  ],\n   [\n  'I am in Omsk',\n  'I am in Siberia',\n  ['I am not in Siberia and  I am not in Omsk.',5],\n  ['It\\'s not true that if I am in Omsk then I am in Siberia.',3],\n  ['If I am  in Omsk then I am in Siberia and  if I am Siberia then I am in Omsk.',12],\n  ['Either I am in Siberia and I am not in Omsk; or I am in Omsk and I am in not Siberia.',13]\n  ]\n  ]", "description": "", "name": "all_exp"}}, "ungrouped_variables": ["choices", "logic_exp", "correctl", "hopel", "gloryl", "all_logic", "faithl", "all_exp", "logicl"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "functions": {}, "showQuestionGroupNames": false, "parts": [{"displayType": "radiogroup", "minMarks": 0, "layout": {"type": "all", "expression": ""}, "choices": ["<p>{choices[0][2][0]}</p>", "<p>{choices[0][3][0]}</p>", "<p>{choices[0][4][0]}</p>", "<p>{choices[0][5][0]}</p>"], "showCorrectAnswer": true, "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0]], "prompt": "<p>Let $p$ and $q$ denote respectively the propositions '{choices[0][0]}'&nbsp;and '{choices[0][1]}'.</p>", "type": "m_n_x", "maxAnswers": 0, "shuffleChoices": true, "warningType": "none", "scripts": {}, "marks": 0, "minAnswers": 0, "maxMarks": 0, "shuffleAnswers": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "answers": ["<p>{logicl[0][0]}</p>", "<p>{logicl[0][1]}</p>", "<p>{logicl[0][2]}</p>", "<p>{logicl[0][3]}</p>", "<p>{logicl[0][4]}</p>", "<p>{logicl[0][5]}</p>", "<p>{logicl[0][6]}</p>", "<p>{logicl[0][7]}</p>", "<p>{logicl[0][8]}</p>"]}, {"displayType": "radiogroup", "minMarks": 0, "layout": {"type": "all", "expression": ""}, "choices": ["<p>{choices[1][2][0]}</p>", "<p>{choices[1][3][0]}</p>", "<p>{choices[1][4][0]}</p>", "<p>{choices[1][5][0]}</p>"], "showCorrectAnswer": true, "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0]], "prompt": "<p>Let $p$ and $q$ denote respectively the propositions '{choices[1][0]}'&nbsp;and '{choices[1][1]}'.</p>", "type": "m_n_x", "maxAnswers": 0, "shuffleChoices": true, "warningType": "none", "scripts": {}, "marks": 0, "minAnswers": 0, "maxMarks": 0, "shuffleAnswers": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "answers": ["<p>{logicl[1][0]}</p>", "<p>{logicl[1][1]}</p>", "<p>{logicl[1][2]}</p>", "<p>{logicl[1][3]}</p>", "<p>{logicl[1][4]}</p>", "<p>{logicl[1][5]}</p>", "<p>{logicl[1][6]}</p>", "<p>{logicl[1][7]}</p>", "<p>{logicl[1][8]}</p>"]}, {"displayType": "radiogroup", "minMarks": 0, "layout": {"type": "all", "expression": ""}, "choices": ["<p>{choices[2][2][0]}</p>", "<p>{choices[2][3][0]}</p>", "<p>{choices[2][4][0]}</p>", "<p>{choices[2][5][0]}</p>"], "showCorrectAnswer": true, "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0]], "prompt": "<p>Let $p$ and $q$ denote respectively the propositions '{choices[2][0]}'&nbsp;and '{choices[2][1]}'.</p>", "type": "m_n_x", "maxAnswers": 0, "shuffleChoices": true, "warningType": "none", "scripts": {}, "marks": 0, "minAnswers": 0, "maxMarks": 0, "shuffleAnswers": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "answers": ["<p>{logicl[2][0]}</p>", "<p>{logicl[2][1]}</p>", "<p>{logicl[2][2]}</p>", "<p>{logicl[2][3]}</p>", "<p>{logicl[2][4]}</p>", "<p>{logicl[2][5]}</p>", "<p>{logicl[2][6]}</p>", "<p>{logicl[2][7]}</p>", "<p>{logicl[2][8]}</p>"]}], "statement": "<p>Choose the correct logical expression&nbsp;&nbsp;for the following English sentences.</p>", "tags": [], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": ""}, {"name": "Quantifiers 2-", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "tags": ["logic", "quantifiers", "statements"], "metadata": {"description": "<p>English sentences which are propositions are given and for each the appropriate proposition&nbsp;&nbsp;involving quantifiers is to be chosen.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>In a seminar group, for group members $m$ and $n$, we let $P(m,n)$ to be the predicate&nbsp;<strong><em>m knows the name of n&nbsp;</em></strong>.</p>\n<p>For each English sentence choose the corresponding proposition involving quantifiers.</p>\n<p>Note that you will lose one mark for every incorrect choice. However, the minimum mark is $0$.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"select": {"name": "select", "group": "Part 0", "definition": "shuffle(list(0..length(all)-1))[0..4]", "description": "", "templateType": "anything", "can_override": false}, "select2": {"name": "select2", "group": "Part 2", "definition": "list(set(0..length(all)-1)-(set(select) or set(select1)))", "description": "", "templateType": "anything", "can_override": false}, "select1": {"name": "select1", "group": "Part 1", "definition": "list(set(0..length(all)-1)-set(select))[0..4]", "description": "", "templateType": "anything", "can_override": false}, "marks_matrix": {"name": "marks_matrix", "group": "Ungrouped variables", "definition": "matrix(list(2*id(4)-matrix(repeat(repeat(1,4),4))))", "description": "", "templateType": "anything", "can_override": false}, "all": {"name": "all", "group": "Ungrouped variables", "definition": "[['There is someone not known to the rest.',\n    '$\\\\exists m \\\\forall n (\\\\neg P(n,m))$'],\n  ['Every group member doesn\\'t know the name of at least one other.',\n    '$\\\\forall m \\\\exists n (\\\\neg P(m,n))$'],\n  ['Nobody knows the name of anybody else.',\n    '$\\\\forall m \\\\forall n (\\\\neg P(m,n))$'],\n  ['There is a pair of group members who do not know each other\\'s name.',\n    '$\\\\exists m \\\\exists n (\\\\neg P(m,n) \\\\land \\\\neg P(n,m)$'],\n  ['There is someone who knows everyone\\'s name.',\n    '$\\\\exists m \\\\forall n (P(m,n))$'],\n  ['There is at least one person who knows the name of somebody else.',\n    '$\\\\exists m \\\\exists n (P(n,m))$'],\n  ['There is someone who doesn\\'t know the name of at least one other group member.',\n    '$\\\\exists m \\\\exists n (\\\\neg P(n,m))$'],\n  ['Someone\\'s name is known to everyone else.',\n    '$\\\\exists m \\\\forall n ( P(n,m))$'],\n  ['There is at least one person who does not know the name of anybody else.',\n    '$\\\\exists m \\\\forall n (\\\\neg P(m,n))$'],\n  ['Everybody knows at least one other person\\'s name.',\n    '$\\\\forall m \\\\exists n (P(m,n))$'],\n  ['Any member of the group has at least one person who doesn\\'t know their name.',\n    '$\\\\forall n \\\\exists m (\\\\neg P(m,n))$'],\n  ['There are at least two people who know each other\\'s name.',\n    '$\\\\exists n \\\\exists m (P(n,m) \\\\land P(m,n))$']\n  \n  ]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["all", "marks_matrix"], "variable_groups": [{"name": "Part 0", "variables": ["select"]}, {"name": "Part 1", "variables": ["select1"]}, {"name": "Part 2", "variables": ["select2"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The numbers heading the columns refer to the following:</p>\n<p><strong>1</strong>. &nbsp;{all[select[0]][1]}</p>\n<p><strong>2</strong>. &nbsp;{all[select[1]][1]}</p>\n<p><strong>3</strong>. &nbsp;{all[select[2]][1]}</p>\n<p><strong>4. &nbsp;</strong>{all[select[3]][1]}</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": "4", "maxAnswers": "4", "shuffleChoices": true, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "warn", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["{all[select[0]][0]}", "{all[select[1]][0]}", "{all[select[2]][0]}", "{all[select[3]][0]}"], "matrix": "marks_matrix", "layout": {"type": "all", "expression": ""}, "answers": ["<p><strong>1</strong></p>", "<p><strong>2</strong></p>", "<p><strong>3</strong></p>", "<p><strong>4</strong></p>"]}, {"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The numbers heading the columns refer to the following:</p>\n<p><strong>1</strong>. &nbsp;{all[select1[0]][1]}</p>\n<p><strong>2</strong>. &nbsp;{all[select1[1]][1]}</p>\n<p><strong>3</strong>. &nbsp;{all[select1[2]][1]}</p>\n<p><strong>4. &nbsp;</strong>{all[select1[3]][1]}</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": "4", "maxAnswers": "4", "shuffleChoices": true, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "warn", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["{all[select1[0]][0]}", "{all[select1[1]][0]}", "{all[select1[2]][0]}", "{all[select1[3]][0]}"], "matrix": "marks_matrix", "layout": {"type": "all", "expression": ""}, "answers": ["<p><strong>1</strong></p>", "<p><strong>2</strong></p>", "<p><strong>3</strong></p>", "<p><strong>4</strong></p>"]}, {"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The numbers heading the columns refer to the following:</p>\n<p><strong>1</strong>. &nbsp;{all[select2[0]][1]}</p>\n<p><strong>2</strong>. &nbsp;{all[select2[1]][1]}</p>\n<p><strong>3</strong>. &nbsp;{all[select2[2]][1]}</p>\n<p><strong>4. &nbsp;</strong>{all[select2[3]][1]}</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": "4", "maxAnswers": "4", "shuffleChoices": true, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "warn", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["{all[select2[0]][0]}", "{all[select2[1]][0]}", "{all[select2[2]][0]}", "{all[select2[3]][0]}"], "matrix": "marks_matrix", "layout": {"type": "all", "expression": ""}, "answers": ["<p><strong>1</strong></p>", "<p><strong>2</strong></p>", "<p><strong>3</strong></p>", "<p><strong>4</strong></p>"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Quantifiers 4--AJD", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "variable_groups": [], "variables": {"Prop_const": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[random(Qchoice),random(Qchoice),random(Qchoice),random(Achoice),random(Bchoice),random(Cchoice)]", "description": "", "name": "Prop_const"}, "wrong_flags": {"templateType": "anything", "group": "Ungrouped variables", "definition": "shuffle([shuffle([0,1,1,1,1]),shuffle([0,0,1,1,1]),shuffle([0,0,0,1,1]),shuffle([0,0,0,0,1])])[0..4]", "description": "", "name": "wrong_flags"}, "prop2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[random(Achoice),random(Bchoice)]", "description": "", "name": "prop2"}, "Cchoice": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[[\"\\\\rightarrow\",\"\\\\land\"],\n  [\"\\\\land\",\"\\\\rightarrow\"]\n  ]", "description": "", "name": "Cchoice"}, "Achoice": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[\n[\"c \\\\ge b\"],\n[\"c < b\"],\n[\"c = b\"],\n[\"c \\\\neq b\"],\n[\"2c\\\\le b\"],\n[\"c\\\\ge b+1\"],\n[\"c < b+1\"],\n[\"2c > b\"]\n]", "description": "", "name": "Achoice"}, "Qchoice": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[\n  [\"\\\\forall\",\"\\\\exists\"],\n  [\"\\\\exists\",\"\\\\forall\"]\n]", "description": "", "name": "Qchoice"}, "Bchoice": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[\n[\"|(-1)\\^c| < a\",\"|(-1)\\^c| \\\\ge a\"],\n[\"\\\\left|\\\\sqrt\\{\\\\left(1-\\\\frac\\{1\\}\\{c\\}\\\\right)\\}-1\\\\right| < a\",\"a \\\\leq \\\\left| \\\\sqrt\\{\\\\left(1-\\\\frac\\{1\\}\\{c\\}\\\\right)\\}-1 \\\\right|\"],\n[\"\\\\frac\\{1\\}\\{2\\^c\\} < 3a\",\"\\\\frac\\{1\\}\\{2\\^c\\} \\\\ge 3a\"],\n[\"\\\\frac\\{c\\^2-2\\}\\{2c+3\\} > 3a+6\",\"\\\\frac\\{c\\^2-2\\}\\{2c+3\\} \\\\le 3a+6\"],\n[\"\\\\left|\\\\frac\\{1\\}\\{c\\^3\\}\\\\right| < a\",\"\\\\left|\\\\frac\\{1\\}\\{c\\^3\\}\\\\right| \\\\ge a\"],\n[\"\\\\frac\\{c\\^2+6\\}\\{2c\\^2+1\\} < a\",\"\\\\frac\\{c\\^2+6\\}\\{2c\\^2+1\\} \\\\ge a\"]\n]\n", "description": "", "name": "Bchoice"}}, "ungrouped_variables": ["Prop_const", "Cchoice", "Achoice", "Qchoice", "Bchoice", "wrong_flags", "prop2"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "functions": {}, "showQuestionGroupNames": false, "parts": [{"displayType": "radiogroup", "choices": ["<p></p>\n<p>$\\displaystyle &nbsp;\\var{latex(Prop_const[0][1])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][1])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][1])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(Prop_const[3][0])})\\, \\var{latex(Prop_const[5][1])}\\, \\left(\\var{latex(Prop_const[4][1])}\\right)\\right]$</p>", "<p>$\\displaystyle &nbsp;\\var{latex(Prop_const[0][wrong_flags[0][0]])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][wrong_flags[0][1]])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][wrong_flags[0][2]])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(Prop_const[3][0])})\\, \\var{latex(Prop_const[5][wrong_flags[0][3]])}\\, \\left(\\var{latex(Prop_const[4][wrong_flags[0][4]])}\\right)\\right]$</p>", "<p>$\\displaystyle \\var{latex(Prop_const[0][wrong_flags[1][0]])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][wrong_flags[1][1]])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][wrong_flags[1][2]])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(Prop_const[3][0])})\\, \\var{latex(Prop_const[5][wrong_flags[1][3]])}\\, \\left(\\var{latex(Prop_const[4][wrong_flags[1][4]])}\\right)\\right]$</p>", "<p>&nbsp;$\\displaystyle &nbsp;\\var{latex(Prop_const[0][wrong_flags[2][0]])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][wrong_flags[2][1]])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][wrong_flags[2][2]])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(Prop_const[3][0])})\\, \\var{latex(Prop_const[5][wrong_flags[2][3]])}\\, \\left(\\var{latex(Prop_const[4][wrong_flags[2][4]])}\\right)\\right]$</p>"], "showCorrectAnswer": true, "displayColumns": "1", "prompt": "<p>Choose the negation of&nbsp;&nbsp; \\[\\var{latex(Prop_const[0][0])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][0])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][0])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(Prop_const[3][0])})\\, \\var{latex(Prop_const[5][0])}\\, \\left(\\var{latex(Prop_const[4][0])}\\right)\\right]\\]</p>\n<p>from the list below</p>", "distractors": ["", "", "", ""], "variableReplacements": [], "shuffleChoices": true, "scripts": {}, "minMarks": 0, "type": "1_n_2", "maxMarks": "4", "variableReplacementStrategy": "originalfirst", "matrix": ["4", 0, 0, 0], "marks": 0}, {"displayType": "radiogroup", "choices": ["<p>$\\displaystyle \\var{latex(Prop_const[0][0])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][1])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][0])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(prop2[0][0])})\\, \\var{latex(Prop_const[5][0])}\\, \\left(\\var{latex(prop2[1][0])}\\right)\\right]$</p>", "<p>$\\displaystyle &nbsp;\\var{latex(Prop_const[0][1-wrong_flags[1][0]])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][wrong_flags[1][1]])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][1-wrong_flags[1][2]])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(prop2[0][0])})\\, \\var{latex(Prop_const[5][1-wrong_flags[1][3]])}\\, \\left(\\var{latex(prop2[1][1-wrong_flags[1][4]])}\\right)\\right]$</p>\n<p></p>", "<p>$\\displaystyle &nbsp;\\var{latex(Prop_const[0][1-wrong_flags[2][0]])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][wrong_flags[2][1]])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][1-wrong_flags[2][2]])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(prop2[0][0])})\\, \\var{latex(Prop_const[5][1-wrong_flags[2][3]])}\\, \\left(\\var{latex(prop2[1][1-wrong_flags[2][4]])}\\right)\\right]$</p>\n<p></p>", "<p>$\\displaystyle &nbsp;\\var{latex(Prop_const[0][1-wrong_flags[3][0]])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][wrong_flags[3][1]])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][1-wrong_flags[3][2]])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(prop2[0][0])})\\, \\var{latex(Prop_const[5][1-wrong_flags[3][3]])}\\, \\left(\\var{latex(prop2[1][1-wrong_flags[3][4]])}\\right)\\right]$</p>"], "showCorrectAnswer": true, "displayColumns": "1", "prompt": "<p>Choose the negation of&nbsp;</p>\n<p>\\[\\var{latex(Prop_const[0][1])} a \\in \\mathbb{R}^+, \\var{latex(Prop_const[1][0])} b \\in \\mathbb{N}, \\var{latex(Prop_const[2][1])} c \\in \\mathbb{N}\\,\\left[(\\var{latex(prop2[0][0])})\\, \\var{latex(Prop_const[5][1])}\\, \\left(\\var{latex(prop2[1][1])}\\right)\\right]\\]</p>\n<p>from the list below</p>", "distractors": ["", "", "", ""], "variableReplacements": [], "shuffleChoices": true, "scripts": {}, "minMarks": 0, "type": "1_n_2", "maxMarks": "4", "variableReplacementStrategy": "originalfirst", "matrix": ["4", 0, 0, 0], "marks": 0}], "statement": "<p></p>\n<p></p>\n<p></p>", "tags": ["exists", "for all", "logic", "logical expressions", "negation of logical expressions", "negation of quantifiers", "predicates", "quantifiers"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Given&nbsp;two propositions&nbsp;in mathematics using quantifiers, choose the corresponding negation of the proposition. For example, the negation of: $\\displaystyle \\exists a \\in \\mathbb{R^+},\\;\\exists b \\in \\mathbb{N},\\;\\exists c \\in \\mathbb{N}\\;\\left[(c \\lt b+1) \\land \\left(\\frac{1}{2^n} \\geq 3a\\right)\\right]$</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": ""}, {"name": "Quantifiers1-", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "variable_groups": [{"variables": ["marking_matrix", "select"], "name": "Part 0"}, {"variables": ["select1", "marking_matrix1"], "name": "Part 1"}, {"variables": ["select2", "marking_matrix2"], "name": "Part 2"}], "variables": {"neg_marks": {"group": "Ungrouped variables", "templateType": "anything", "definition": "2*id(3)+matrix(map(map(-1,x,0..2),y,0..2))", "name": "neg_marks", "description": ""}, "marking_matrix1": {"group": "Part 1", "templateType": "anything", "definition": "map(list(neg_marks[x])+[all[select1[x]][2]]+[-1*all[select1[x]][2]],x,0..2)", "name": "marking_matrix1", "description": ""}, "marking_matrix": {"group": "Part 0", "templateType": "anything", "definition": "map(list(neg_marks[x])+[all[select[x]][2]]+[-1*all[select[x]][2]],x,0..2)", "name": "marking_matrix", "description": ""}, "select1": {"group": "Part 1", "templateType": "anything", "definition": "list(set(0..length(all)-1)-set(select))[0..3]", "name": "select1", "description": ""}, "select": {"group": "Part 0", "templateType": "anything", "definition": "shuffle(list(0..length(all)-1))[0..3]", "name": "select", "description": ""}, "all": {"group": "Ungrouped variables", "templateType": "anything", "definition": "[['The square of any real number is greater than $0$.',\n    '$\\\\forall x \\\\in \\\\mathbb{R}\\\\;(x^2\\\\gt 0).$',-1],\n  ['Given a real number then some integral power is not negative.',\n    '$\\\\forall x \\\\in \\\\mathbb{R} \\\\;\\\\exists n \\\\in \\\\mathbb{N}\\\\;(x^n\\\\geq 0).$',1],\n  ['A subset of the natural numbers is a subset of the reals.',\n    '$\\\\forall X \\\\subseteq \\\\mathbb{N}\\\\;(X\\\\subseteq \\\\mathbb{R}).$',1],\n  ['For every natural number $n$ there is a subset of $\\\\mathbb{N}$ with less than $n$ members.',\n    '$\\\\forall n \\\\in \\\\mathbb{N}\\\\;\\\\exists X \\\\subseteq \\\\mathbb{N}\\\\;(|X|\\\\lt n).$',1],\n  ['All subsets of the natural numbers have less than a fixed number of elements.',\n    '$\\\\exists n \\\\in \\\\mathbb{N}\\\\; \\\\forall X \\\\subseteq \\\\mathbb{N}\\\\;(|X|\\\\lt n).$',-1],\n  ['All subsets of the natural numbers are finite.',\n    '$\\\\forall X \\\\subseteq \\\\mathbb{N}\\\\;\\\\exists n \\\\in \\\\mathbb{Z}\\\\;(|X|=n).$',-1],\n  ['Given an integer $n$, there is a subset of the natural numbers with $n$ elements.',\n    '$\\\\forall n \\\\in \\\\mathbb{Z}\\\\;\\\\exists X \\\\subseteq \\\\mathbb{N}\\\\;(|X|=n).$',-1],\n  ['Given an integer, then adding $5$ to it gives another integer.',\n    '$\\\\forall n \\\\in \\\\mathbb{Z}\\\\; \\\\exists m \\\\in \\\\mathbb{Z}\\\\; (m=n+5).$',1],\n  ['There is an integer $t$ such that adding $5$ to any integer gives $t$.',\n    '$\\\\exists m \\\\in \\\\mathbb{Z}\\\\; \\\\forall n \\\\in \\\\mathbb{Z}\\\\; (m=n+5).$',-1]\n  ]", "name": "all", "description": ""}, "select2": {"group": "Part 2", "templateType": "anything", "definition": "list(set(0..length(all)-1)-(set(select) or set(select1)))", "name": "select2", "description": ""}, "marking_matrix2": {"group": "Part 2", "templateType": "anything", "definition": "map(list(neg_marks[x])+[all[select2[x]][2]]+[-1*all[select2[x]][2]],x,0..2)", "name": "marking_matrix2", "description": ""}}, "ungrouped_variables": ["all", "neg_marks"], "rulesets": {}, "showQuestionGroupNames": false, "functions": {}, "parts": [{"displayType": "checkbox", "layout": {"type": "all", "expression": ""}, "choices": ["{all[select[0]][0]}", "{all[select[1]][0]}", "{all[select[2]][0]}"], "showCorrectAnswer": true, "matrix": "marking_matrix", "minAnswers": "6", "maxAnswers": "6", "shuffleChoices": true, "warningType": "warn", "scripts": {}, "minMarks": 0, "type": "m_n_x", "maxMarks": 0, "shuffleAnswers": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "answers": ["{all[select[0]][1]}", "{all[select[1]][1]}", "{all[select[2]][1]}", "True", "False"]}, {"displayType": "checkbox", "layout": {"type": "all", "expression": ""}, "choices": ["{all[select1[0]][0]}", "{all[select1[1]][0]}", "{all[select1[2]][0]}"], "showCorrectAnswer": true, "matrix": "marking_matrix1", "minAnswers": "6", "maxAnswers": "6", "shuffleChoices": true, "warningType": "warn", "scripts": {}, "minMarks": 0, "type": "m_n_x", "maxMarks": 0, "shuffleAnswers": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "answers": ["{all[select1[0]][1]}", "{all[select1[1]][1]}", "{all[select1[2]][1]}", "True", "False"]}, {"displayType": "checkbox", "layout": {"type": "all", "expression": ""}, "choices": ["{all[select2[0]][0]}", "{all[select2[1]][0]}", "{all[select2[2]][0]}"], "showCorrectAnswer": true, "matrix": "marking_matrix2", "minAnswers": "6", "maxAnswers": "6", "shuffleChoices": true, "warningType": "warn", "scripts": {}, "minMarks": 0, "type": "m_n_x", "maxMarks": 0, "shuffleAnswers": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "answers": ["{all[select2[0]][1]}", "{all[select2[1]][1]}", "{all[select2[2]][1]}", "True", "False"]}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Choose the appropriate proposition&nbsp;&nbsp;for the following English sentences. Also choose whether they are true or false.</p>\n<p>You must make $2$ choices in each row, one of which is to determine whether the proposition&nbsp;&nbsp;is true or false.</p>\n<p>Note also that every wrong answer takes away one from your score. However, your minimum score is $0$.</p>", "tags": ["logic", "quantifiers", "statements"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>English sentences are given and for each the appropriate proposition&nbsp;involving quantifiers is to be chosen. Also choose whether the propositions are true or false.</p>"}, "advice": ""}, {"name": "set1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "variable_groups": [], "variables": {"r": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(8..15)", "description": "", "name": "r"}, "answer_set4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "answer_set1 and answer_set3", "description": "", "name": "answer_set4"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(8..20)", "description": "", "name": "a"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..7)", "description": "", "name": "c"}, "f": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(10..25)", "description": "", "name": "f"}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-25..-5)", "description": "", "name": "d"}, "g": {"templateType": "anything", "group": "Ungrouped variables", "definition": "r^2", "description": "", "name": "g"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a+random(12..30)", "description": "", "name": "b"}, "answer_set1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "set(mod_set(a,b,c))", "description": "", "name": "answer_set1"}, "answer_set2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "set(-r+1..r-1)and set(d..f)", "description": "", "name": "answer_set2"}, "answer_set3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "set(d..f) and(set(d-1..-r-1) or set(r+1..f+1))", "description": "", "name": "answer_set3"}}, "ungrouped_variables": ["a", "b", "c", "answer_set1", "d", "f", "g", "answer_set2", "r", "answer_set3", "answer_set4"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "functions": {"mod_set": {"type": "list", "language": "javascript", "definition": "//returns all integers which are divisible by c betweeen a and b\nvar l=[];\nfor(var i=a;i<b+1;i++) \n{ if (i%c==0){l.push(i);}\n}\nreturn l;\n", "parameters": [["a", "number"], ["b", "number"], ["c", "number"]]}}, "showQuestionGroupNames": false, "parts": [{"prompt": "<p>a) $A=\\{x \\in \\mathbb{N}\\;|\\;\\var{a} \\leq x \\leq \\var{b}\\text{ and } x \\text{ is divisible by }\\var{c}\\}$.</p>\n<p>$A=\\;$[[0]]</p>\n<p>b) $B=\\{x \\in \\mathbb{Z}\\;|\\;\\var{d} \\leq x \\leq \\var{f}\\text{ and } x^2 \\lt \\var{g}\\}$.</p>\n<p>$B=\\;$[[1]]</p>\n<p>c) $C=\\{x \\in \\mathbb{Z}\\;|\\;\\var{d} \\leq x \\leq \\var{f}\\text{ and } x^2 \\gt \\var{g}\\}$.</p>\n<p>$C=\\;$[[2]]</p>\n<p>d) $A \\cap C=\\;$[[3]]</p>\n<p></p>\n<p>Note that you input sets in the form <code>set(a,b,c,..,z)</code> .</p>\n<p>For example <code> set(1,2,3)</code>gives the set $\\{1,2,3\\}$.</p>\n<p>The empty set is input as&nbsp;<code>set()</code>.</p>\n<p>Also some labour saving tips:</p>\n<p>If you want to input all integers between $a$ and $b$ inclusive then instead of writing all the elements you can input this as <code>set(a..b)</code>.</p>\n<p>If you want to input all integers between $a$ and $b$ inclusive in steps of $c$ then this is input as <code>set(a..b#c)</code>. So all odd integers from $-3$ to $28$ are input as&nbsp;<code>set(-3..28#2).</code></p>", "scripts": {}, "gaps": [{"answer": "{answer_set1}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}, {"answer": "{answer_set2}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}, {"answer": "{answer_set3}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}, {"answer": "{answer_set4}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Write the following sets in enumerated form.</p>\n<p>Note that you enter an enumerated set such as $\\{35,67,99\\}$ as <code>set(35,67,99)</code>.</p>\n<p></p>", "tags": [], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": ""}, "advice": ""}, {"name": "set4-", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "variable_groups": [], "variables": {"ans2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "ans1 and set(1..b)", "name": "ans2", "description": ""}, "ans3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "set(ceil((c1-b1)/a1)..floor((c1+b1)/a1))", "name": "ans3", "description": ""}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..6)", "name": "a", "description": ""}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..8)", "name": "c", "description": ""}, "b1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(6..10 except b)", "name": "b1", "description": ""}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..6 except a)", "name": "a1", "description": ""}, "b2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..12)", "name": "b2", "description": ""}, "b3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..12)", "name": "b3", "description": ""}, "ans4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "ans3 and set(1..floor((c1+b1)/a1))", "name": "ans4", "description": ""}, "c2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(4..10)", "name": "c2", "description": ""}, "c1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..6 except c)", "name": "c1", "description": ""}, "a3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..15)", "name": "a3", "description": ""}, "ans1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "set(a*ceil((c-b)/a)-c..a*floor((c+b)/a)-c#a)", "name": "ans1", "description": ""}, "c3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(6..10)", "name": "c3", "description": ""}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..10)", "name": "b", "description": ""}, "g": {"templateType": "anything", "group": "Ungrouped variables", "definition": "gcd(a3,b3)", "name": "g", "description": ""}, "a2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..6)", "name": "a2", "description": ""}}, "ungrouped_variables": ["a", "b", "c", "ans1", "ans2", "a1", "b1", "c1", "ans3", "ans4", "a2", "b2", "c2", "a3", "b3", "c3", "g"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "showQuestionGroupNames": false, "functions": {}, "parts": [{"showCorrectAnswer": true, "scripts": {}, "gaps": [{"answer": "{ans1}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}, {"answer": "{ans2}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}, {"answer": "{ans3}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}, {"answer": "{ans4}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "<p>1) $S=\\{y\\;|\\;y \\in \\mathbb{Z}, y=\\var{a}x-\\var{c},\\;x \\in \\mathbb{Z}\\text{ and } |y| \\leq \\var{b}\\}$</p>\n<p>$S\\;$=[[0]]</p>\n<p>2) $S=\\{y\\;|\\;y \\in \\mathbb{N}, y=\\var{a}x-\\var{c},\\;x \\in \\mathbb{Z}\\text{ and } |y| \\leq \\var{b}\\}$</p>\n<p>$S\\;$=[[1]]</p>\n<p>3)&nbsp;$S=\\{x\\:| x \\in \\mathbb{Z}\\text{ and }\\;|\\var{a1}x-\\var{c1}| \\leq \\var{b1}\\}$.</p>\n<p>$S=\\;$[[2]]</p>\n<p>4) $S=\\{x\\:| x \\in \\mathbb{N}\\text{ and }\\;|\\var{a1}x-\\var{c1}| \\leq \\var{b1}\\}$.</p>\n<p>$S=\\;$[[3]]</p>", "variableReplacements": [], "marks": 0}, {"showCorrectAnswer": true, "scripts": {}, "gaps": [{"answer": "{set(-c2+1..c2-1)}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}, {"answer": "{set(g*ceil((-c3+1)/g)..(c3-1)#g)}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "<p>1) $S=\\{\\var{a2}a+\\var{b2}b\\;|\\;a,\\;b \\in \\mathbb{Z},\\;|\\var{a2}a+\\var{b2}b\\,|\\lt \\var{c2}\\}$.</p>\n<p>$S=\\;$[[0]]</p>\n<p>2) $S=\\{\\var{a3}a+\\var{b3}b\\;|\\;a,\\;b \\in \\mathbb{Z},\\;|\\var{a3}a+\\var{b3}b\\,|\\lt \\var{c3}\\}$.</p>\n<p>$S=\\;$[[1]]</p>\n<p></p>", "variableReplacements": [], "marks": 0}], "statement": "<p>Enumerate each of the following sets.</p>\n<p></p>\n<p>Note that you input sets in the form <code>set(a,b,c,..,z)</code> .</p>\n<p>For example <code> set(1,2,3)</code>gives the set $\\{1,2,3\\}$.</p>\n<p>The empty set is input as&nbsp;<code>set()</code>.</p>\n<p>Also some labour saving tips:</p>\n<p>If you want to input all integers between $a$ and $b$ inclusive then instead of writing all the elements you can input this as <code>set(a..b)</code>.</p>\n<p>If you want to input all integers between $a$ and $b$ inclusive in steps of $c$ then this is input as <code>set(a..b#c)</code>. So all odd integers from $-3$ to $28$ are input as&nbsp;<code>set(-3..28#2).</code></p>", "tags": [], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": ""}, "variablesTest": {"condition": "gcd(a2,b2)=1 and gcd(a3,b3)<>1", "maxRuns": "200"}, "advice": ""}], "pickingStrategy": "all-ordered", "pickQuestions": 0, "name": ""}], "type": "exam", "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "showfrontpage": true, "preventleave": true, "browse": true, "showresultspage": "oncompletion"}, "showQuestionGroupNames": false, "feedback": {"showtotalmark": true, "advicethreshold": 0, "showanswerstate": true, "allowrevealanswer": true, "showactualmark": true}, "name": "Blathnaid's copy of Predicates, Quantifiers and sets", "timing": {"timedwarning": {"action": "none", "message": ""}, "allowPause": true, "timeout": {"action": "none", "message": ""}}, "pickQuestions": 0, "allQuestions": true, "contributors": [{"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "custom_part_types": []}