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.\"
\nFor each English sentence given below, choose the correct proposition involving quantifiers.
", "advice": "When the symbol $\\forall$ appears, read it as \"for all\" or \"for every\".
\nWhen the symbol $\\exists$ appears, read it as \"there exists\" or \"for some (particular)\".
\nKeep in mind that the order these symbols appear in matters! You can think of the first term making $m$ the \"subject\" of the sentence and the second term making $n$ the \"object\" of the sentence.
", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"select1": {"name": "select1", "group": "Ungrouped variables", "definition": "list(set(0..length(all)-1)-set(select))[0..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}, "marks": {"name": "marks", "group": "Ungrouped variables", "definition": "matrix(list(0.5id(3)-0.25matrix(repeat(repeat(1,3),3))))", "description": "", "templateType": "anything", "can_override": false}, "select2": {"name": "select2", "group": "Ungrouped variables", "definition": "list(set(0..length(all)-1)-(set(select) or set(select1)))", "description": "", "templateType": "anything", "can_override": false}, "select": {"name": "select", "group": "Part 0", "definition": "shuffle(list(0..length(all)-1))[0..4]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["all", "marks", "select1", "select2"], "variable_groups": [{"name": "Part 0", "variables": ["select"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": "4", "minAnswers": "0", "maxAnswers": "4", "shuffleChoices": true, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": false, "markingMethod": "sum ticked cells", "choices": ["{all[select[0]][0]}", "{all[select[1]][0]}", "{all[select[2]][0]}", "{all[select[3]][0]}"], "matrix": "marks", "layout": {"type": "all", "expression": ""}, "answers": ["{all[select[0]][1]}
", "{all[select[1]][1]}
{all[select[2]][1]}