Let $p$ and $q$ denote respectively the propositions '{choices[0][0]}' and '{choices[0][1]}'.
", "matrix": "mm0", "shuffleAnswers": true, "minAnswers": 0, "marks": 0, "variableReplacements": [], "answers": ["{logic_exp[0]}", "{logic_exp[1]}", "{logic_exp[2]}", "{logic_exp[3]}", "{logic_exp[4]}", "{logic_exp[5]}", "{logic_exp[6]}", "{logic_exp[7]}", "{logic_exp[8]}"], "choices": ["{choices[0][2]}", "{choices[0][3]}", "{choices[0][4]}", "{choices[0][5]}"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "warningType": "none", "showCorrectAnswer": true, "type": "m_n_x", "shuffleChoices": true, "minMarks": 0, "layout": {"type": "all", "expression": ""}}, {"maxAnswers": 0, "prompt": "Let $p$ and $q$ denote respectively the propositions '{choices[1][0]}' and '{choices[1][1]}'.
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", "matrix": "mm2", "shuffleAnswers": true, "minAnswers": 0, "marks": 0, "variableReplacements": [], "answers": ["{logic_exp[0]}", "{logic_exp[1]}", "{logic_exp[2]}", "{logic_exp[3]}", "{logic_exp[4]}", "{logic_exp[5]}", "{logic_exp[6]}", "{logic_exp[7]}", "{logic_exp[8]}"], "choices": ["{choices[2][2]}", "{choices[2][3]}", "{choices[2][4]}", "{choices[2][5]}"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "warningType": "none", "showCorrectAnswer": true, "type": "m_n_x", "shuffleChoices": true, "minMarks": 0, "layout": {"type": "all", "expression": ""}}], "statement": "Choose the correct logical expression for the following English sentences.
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"mm1": {"definition": "map(map(if(choices[1][6][y]=x,1,0),x,0..8),y,0..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "mm1", "description": ""}, "mm0": {"definition": "map(map(if(choices[0][6][y]=x,1,0),x,0..8),y,0..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "mm0", "description": ""}, "mm2": {"definition": "map(map(if(choices[2][6][y]=x,1,0),x,0..8),y,0..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "mm2", "description": ""}, "t": {"definition": "random(0,1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "choices": {"definition": "[['It is snowing','I will go skiing',\n 'As it is not snowing I will go skiing.',\n 'It will snow if I don\\'t go skiing.',\n 'I will go skiing if it is snowing.',\n 'It is snowing and I may or may not go skiing.',\n [2,8,4,6,0,1,3,7,5]\n ],\n ['I am working at my studies', 'I am in the library',\n 'I am working at my studies in the library.',\n 'If I use the library then I am working at my studies.',\n 'If I am working at my studies then I am not in the library.',\n 'If I am in the library then I may not be working at my studies.',\n [1,7,0,6,8,2,3,4,5]\n ],\n ['It is sunny','I will carry an umbrella',\n 'If it is not sunny then I will carry an umbrella.',\n 'I carry an umbrella even if it is sunny.',\n 'If it is sunny then I may carry an umbrella.',\n 'If I carry an umbrella then the day always turns out to be sunny!',\n [8,4,6,7,0,1,2,5,3]\n \n]\n \n]", "templateType": "anything", "group": "Ungrouped variables", "name": "choices", "description": ""}, "logic_exp": {"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 ]", "templateType": "anything", "group": "Ungrouped variables", "name": "logic_exp", "description": ""}}, "metadata": {"notes": "", "description": "Given sentences involving propositions translate into logical expressions.
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Quantifiers 2-", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "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/"}], "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 .
\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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\n1. {all[select1[0]][1]}
\n2. {all[select1[1]][1]}
\n3. {all[select1[2]][1]}
\n4. {all[select1[3]][1]}
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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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