// Numbas version: finer_feedback_settings
{"name": "Quantifiers 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["all", "marks"], "name": "Quantifiers 2", "tags": ["logic", "quantifiers", "statements"], "advice": "", "rulesets": {}, "parts": [{"maxAnswers": "4", "shuffleChoices": true, "matrix": "marks", "shuffleAnswers": false, "minAnswers": "4", "marks": 0, "variableReplacements": [], "answers": ["{all[select[0]][1]}", "{all[select[1]][1]}", "{all[select[2]][1]}", "{all[select[3]][1]}"], "choices": ["{all[select[0]][0]}", "{all[select[1]][0]}", "{all[select[2]][0]}", "{all[select[3]][0]}"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "warningType": "warn", "showCorrectAnswer": true, "type": "m_n_x", "minMarks": 0, "layout": {"type": "all", "expression": ""}}, {"maxAnswers": "4", "shuffleChoices": true, "matrix": "marks", "shuffleAnswers": false, "minAnswers": "4", "marks": 0, "variableReplacements": [], "answers": ["{all[select1[0]][1]}", "{all[select1[1]][1]}", "{all[select1[2]][1]}", "{all[select1[3]][1]}"], "choices": ["{all[select1[0]][0]}", "{all[select1[1]][0]}", "{all[select1[2]][0]}", "{all[select1[3]][0]}"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "warningType": "warn", "showCorrectAnswer": true, "type": "m_n_x", "minMarks": 0, "layout": {"type": "all", "expression": ""}}, {"maxAnswers": "4", "shuffleChoices": true, "matrix": "marks", "shuffleAnswers": false, "minAnswers": "4", "marks": 0, "variableReplacements": [], "answers": ["{all[select2[0]][1]}", "{all[select2[1]][1]}", "{all[select2[2]][1]}", "{all[select2[3]][1]}"], "choices": ["{all[select2[0]][0]}", "{all[select2[1]][0]}", "{all[select2[2]][0]}", "{all[select2[3]][0]}"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "warningType": "warn", "showCorrectAnswer": true, "type": "m_n_x", "minMarks": 0, "layout": {"type": "all", "expression": ""}}], "statement": "<p>In a seminar group we let $P(m,n)$ for group members $m$ and $n$ 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>", "variable_groups": [{"variables": ["select"], "name": "Part 0"}, {"variables": ["select1"], "name": "Part 1"}, {"variables": ["select2"], "name": "Part 2"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"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  ]", "templateType": "anything", "group": "Ungrouped variables", "name": "all", "description": ""}, "marks": {"definition": "matrix(list(2*id(4)-matrix(repeat(repeat(1,4),4))))", "templateType": "anything", "group": "Ungrouped variables", "name": "marks", "description": ""}, "select2": {"definition": "list(set(0..length(all)-1)-(set(select) or set(select1)))", "templateType": "anything", "group": "Part 2", "name": "select2", "description": ""}, "select1": {"definition": "list(set(0..length(all)-1)-set(select))[0..4]", "templateType": "anything", "group": "Part 1", "name": "select1", "description": ""}, "select": {"definition": "shuffle(list(0..length(all)-1))[0..4]", "templateType": "anything", "group": "Part 0", "name": "select", "description": ""}}, "metadata": {"notes": "", "description": "<p>English sentences which are propositions are given and for each the appropriate statement involving quantifiers is to be chosen.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}], "resources": []}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}