// Numbas version: exam_results_page_options
{"name": "Luis's copy of Quantifiers 4--AJD", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": ["exists", "for all", "logic", "logical expressions", "negation of logical expressions", "negation of quantifiers", "predicates", "quantifiers"], "statement": "<p></p>\n<p></p>\n<p></p>", "name": "Luis's copy of Quantifiers 4--AJD", "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>"}, "ungrouped_variables": ["Prop_const", "Cchoice", "Achoice", "Qchoice", "Bchoice", "wrong_flags", "prop2"], "parts": [{"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>", "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>"], "variableReplacements": [], "showCorrectAnswer": true, "displayColumns": "1", "matrix": ["4", 0, 0, 0], "variableReplacementStrategy": "originalfirst", "minMarks": 0, "maxMarks": "4", "scripts": {}, "distractors": ["", "", "", ""], "type": "1_n_2", "shuffleChoices": true, "marks": 0}, {"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>", "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>"], "variableReplacements": [], "showCorrectAnswer": true, "displayColumns": "1", "matrix": ["4", 0, 0, 0], "variableReplacementStrategy": "originalfirst", "minMarks": 0, "maxMarks": "4", "scripts": {}, "distractors": ["", "", "", ""], "type": "1_n_2", "shuffleChoices": true, "marks": 0}], "variables": {"Qchoice": {"definition": "[\n  [\"\\\\forall\",\"\\\\exists\"],\n  [\"\\\\exists\",\"\\\\forall\"]\n]", "name": "Qchoice", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "prop2": {"definition": "[random(Achoice),random(Bchoice)]", "name": "prop2", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "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]", "name": "wrong_flags", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "Cchoice": {"definition": "[[\"\\\\rightarrow\",\"\\\\land\"],\n  [\"\\\\land\",\"\\\\rightarrow\"]\n  ]", "name": "Cchoice", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "Prop_const": {"definition": "[random(Qchoice),random(Qchoice),random(Qchoice),random(Achoice),random(Bchoice),random(Cchoice)]", "name": "Prop_const", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "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", "name": "Bchoice", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "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]", "name": "Achoice", "templateType": "anything", "group": "Ungrouped variables", "description": ""}}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "type": "question", "rulesets": {}, "advice": "", "showQuestionGroupNames": false, "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}