// Numbas version: exam_results_page_options {"name": "Quantifiers 2-", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Quantifiers 2-", "tags": ["logic", "quantifiers", "statements"], "metadata": {"description": "

English sentences which are propositions are given and for each the appropriate proposition involving quantifiers is to be chosen.

", "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 .

For each English sentence choose the corresponding proposition involving quantifiers.

Note that you will lose one mark for every incorrect choice. However, the minimum mark is $0$.

", "advice": "", "rulesets": {}, "extensions": [], "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": "

The numbers heading the columns refer to the following:

1. {all[select[0]][1]}

2. {all[select[1]][1]}

3. {all[select[2]][1]}

4. {all[select[3]][1]}

", "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": ["

", "

"]}, {"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": "

The numbers heading the columns refer to the following:

1. {all[select1[0]][1]}

2. {all[select1[1]][1]}

3. {all[select1[2]][1]}

4. {all[select1[3]][1]}

", "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": ["

", "

The numbers heading the columns refer to the following:

1. {all[select2[0]][1]}

2. {all[select2[1]][1]}

3. {all[select2[2]][1]}

4. {all[select2[3]][1]}

", "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": ["

", "

"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "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/"}]}]}], "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/"}]}