Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Which of the following are propositions?
", "advice": "For the above we have:
\n1. {all[select[0]][0]}
\n{all[select[0]][1]}
\n2. {all[select[1]][0]}
\n{all[select[1]][1]}
\n3. {all[select[2]][0]}
\n{all[select[2]][1]}
\n4. {all[select[3]][0]}
\n{all[select[3]][1]}
\n5. {all[select[4]][0]}
\n{all[select[4]][1]}
\n6. {all[select[5]][0]}
\n{all[select[5]][1]}
", "rulesets": {}, "variables": {"all": {"name": "all", "group": "Ungrouped variables", "definition": "[\n['Every real number is an even integer.','This is a proposition. It is false as there are real numbers which are not even integers, e.g. $1$.',1],\n ['Every even integer is a real number.','A proposition and true.',1],\n ['If $x$ and $y$ are real numbers and $5x=5y$, then $x=y$.','A true proposition as we can cancel off the 5s.',1],\n ['Lions and tigers.','This is not a proposition as there is no truth value we can determine.',0],\n ['Lions and tigers are animals.','This is a true proposition, at least in the standard interpretation of the words.',1],\n ['Some sets are finite.','A true proposition as, for example, the set $\\\\\\{1 \\\\\\}$ is finite.',1],\n ['The derivative of any polynomial of degree $5$ is a polynomial of degree $6$.','This is a false proposition (as the derivative is of degree $4$).',1],\n ['The smallest positive whole number is 2.','This is a proposition and false, as the smallest positive whole number is $1$.',1],\n ['$\\\\cos(x)=-1$.','This is not a proposition: its truth depends on the value of $x$.',0],\n ['If $n$ is a real number and $n$ is not zero then $n/n=1$.','This a proposition: it is true.',1],\n ['The integer $x$ is a multiple of $7$.','Not a proposition. Its truth depends on the value of $x$.',0],\n ['If the integer $x$ is a multiple of $7$, then it is divisible by $7$.','A true proposition.',1],\n ['Either the integer $x$ is a multiple of $7$, or it is not.','A proposition and true.',1],\n ['Call me Ishmael.','Not a proposition as we cannot ascertain a truth value.',0],\n ['Either $x>3$ or $x<0$.','Not a proposition: its truth depends on the value of $x$.',0],\n ['They like fishcakes.','Not a proposition. Its truth depends on who \"They\" are.',0],\n ['In the beginning.','Not a proposition: is neither true nor false.',0],\n ['Maths is a much better subject to study.','Not a proposition. It depends on what \"better\" refers to.',0],\n ['To be or not to be.','Not a proposition: is neither true nor false.',0],\n ['Leeds football club is at its peak.','Not a proposition. It depends on when it is said, and what \"peak\" means.',0],\n ['If $3x^2-2=0$ then $x=\\\\sqrt{2/3}$ or $x=-\\\\sqrt{2/3}$','A proposition. It does not depend what $x$ is. It is true.',1],\n ['Numbers $x$, $y$ and $z$ have the property that $x+y=z$.','Not a proposition, as its truth depends on the values of $x$, $y$ and $z$.',0],\n ['Numbers $x$, $y$ and $z$ have the property that $x+y>z$ or $x+y \\\\le z$.', 'A proposition. One or other of the conditions holds.',1] \n ]", "description": "", "templateType": "anything"}, "marking_matrix": {"name": "marking_matrix", "group": "Ungrouped variables", "definition": "map([all[x][2],(all[x][2])*(-1)+1],x,select)", "description": "", "templateType": "anything"}, "select": {"name": "select", "group": "Ungrouped variables", "definition": "shuffle(list(0..length(all)-1))[0..6]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["all", "select", "marking_matrix"], "variable_groups": [], "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, "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "choices": ["{all[select[0]][0]}", "{all[select[1]][0]}", "{all[select[2]][0]}", "{all[select[3]][0]}", "{all[select[4]][0]}", "{all[select[5]][0]}"], "matrix": "marking_matrix", "layout": {"type": "all", "expression": ""}, "answers": ["Proposition", "Not a proposition"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"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": ["{choices[0][2][0]}
", "{choices[0][3][0]}
", "{choices[0][4][0]}
", "{choices[0][5][0]}
"], "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": "Let $p$ and $q$ denote respectively the propositions '{choices[0][0]}' and '{choices[0][1]}'.
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", "{logicl[0][1]}
", "{logicl[0][2]}
", "{logicl[0][3]}
", "{logicl[0][4]}
", "{logicl[0][5]}
", "{logicl[0][6]}
", "{logicl[0][7]}
", "{logicl[0][8]}
"]}, {"displayType": "radiogroup", "minMarks": 0, "layout": {"type": "all", "expression": ""}, "choices": ["{choices[1][2][0]}
", "{choices[1][3][0]}
", "{choices[1][4][0]}
", "{choices[1][5][0]}
"], "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": "Let $p$ and $q$ denote respectively the propositions '{choices[1][0]}' and '{choices[1][1]}'.
", "type": "m_n_x", "maxAnswers": 0, "shuffleChoices": true, "warningType": "none", "scripts": {}, "marks": 0, "minAnswers": 0, "maxMarks": 0, "shuffleAnswers": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "answers": ["{logicl[1][0]}
", "{logicl[1][1]}
", "{logicl[1][2]}
", "{logicl[1][3]}
", "{logicl[1][4]}
", "{logicl[1][5]}
", "{logicl[1][6]}
", "{logicl[1][7]}
", "{logicl[1][8]}
"]}, {"displayType": "radiogroup", "minMarks": 0, "layout": {"type": "all", "expression": ""}, "choices": ["{choices[2][2][0]}
", "{choices[2][3][0]}
", "{choices[2][4][0]}
", "{choices[2][5][0]}
"], "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": "Let $p$ and $q$ denote respectively the propositions '{choices[2][0]}' and '{choices[2][1]}'.
", "type": "m_n_x", "maxAnswers": 0, "shuffleChoices": true, "warningType": "none", "scripts": {}, "marks": 0, "minAnswers": 0, "maxMarks": 0, "shuffleAnswers": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "answers": ["{logicl[2][0]}
", "{logicl[2][1]}
", "{logicl[2][2]}
", "{logicl[2][3]}
", "{logicl[2][4]}
", "{logicl[2][5]}
", "{logicl[2][6]}
", "{logicl[2][7]}
", "{logicl[2][8]}
"]}], "statement": "Choose the correct logical expression for the following English sentences.
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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "In a seminar group, for group members $m$ and $n$, we let $P(m,n)$ to be the predicate m knows the name of n .
\nFor each English sentence choose the corresponding proposition involving quantifiers.
\nNote that you will lose one mark for every incorrect choice. However, the minimum mark is $0$.
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\n1. {all[select[0]][1]}
\n2. {all[select[1]][1]}
\n3. {all[select[2]][1]}
\n4. {all[select[3]][1]}
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", "2
", "3
", "4
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\n1. {all[select1[0]][1]}
\n2. {all[select1[1]][1]}
\n3. {all[select1[2]][1]}
\n4. {all[select1[3]][1]}
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", "2
", "3
", "4
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\n1. {all[select2[0]][1]}
\n2. {all[select2[1]][1]}
\n3. {all[select2[2]][1]}
\n4. {all[select2[3]][1]}
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