// Numbas version: finer_feedback_settings
{"name": "Propositional Logic 2", "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "questions": [{"name": "Alexander's copy of Truth tables 0 (v2) (w/ implication)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Alexander Corner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5328/"}], "tags": [], "metadata": {"description": "<p>Create a truth table for a logical expression of the form $a \\operatorname{op} b$ where $a, \\;b$ can be the Boolean variables $p,\\;q,\\;\\neg p,\\;\\neg q$ and $\\operatorname{op}$ one of $\\lor,\\;\\land,\\;\\to$.</p>\n<p>For example $\\neg q \\to \\neg p$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>In the following question you are asked to construct a truth table for:</p>\n<p>\\[\\var{a} \\var{op} \\var{b}.\\]</p>\n<p></p>\n<p><strong>Enter T&nbsp;if true, else enter F.</strong></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>", "advice": "<p>Here is the truth table.</p>\n<table border=\"1\">\n<tbody>\n<tr><th>$p$</th><th>$q$</th><th>$\\var{a} \\var{op} \\var{b}$</th></tr>\n<tr>\n<td>$\\var{disp[0]}$</td>\n<td>$\\var{disq[0]}$</td>\n<td>$\\var{ev1[0]}$</td>\n</tr>\n<tr>\n<td>$\\var{disp[1]}$</td>\n<td>$\\var{disq[1]}$</td>\n<td>$\\var{ev1[1]}$</td>\n</tr>\n<tr>\n<td>$\\var{disp[2]}$</td>\n<td>$\\var{disq[2]}$</td>\n<td>$\\var{ev1[2]}$</td>\n</tr>\n<tr>\n<td>$\\var{disp[3]}$</td>\n<td>$\\var{disq[3]}$</td>\n<td>$\\var{ev1[3]}$</td>\n</tr>\n</tbody>\n</table>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"disp": {"name": "disp", "group": "Truth values", "definition": "bool_to_label(p)", "description": "", "templateType": "anything", "can_override": false}, "q": {"name": "q", "group": "Truth values", "definition": "[true,false,true,false]", "description": "", "templateType": "anything", "can_override": false}, "disq": {"name": "disq", "group": "Truth values", "definition": "bool_to_label(q)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "First Bracket", "definition": "latex(switch(a=\"p\",\"\\\\neg q\",a=\"q\",\"\\\\neg p\",a=\"\\\\neg p\",random(\"q\",\"\\\\neg q\"),random(\"p\",\"\\\\neg p\")))", "description": "", "templateType": "anything", "can_override": false}, "op": {"name": "op", "group": "First Bracket", "definition": "latex(random(\"\\\\to\"))", "description": "", "templateType": "anything", "can_override": false}, "latex_symbol_list": {"name": "latex_symbol_list", "group": "Lists of symbols", "definition": "[\"p\",\"q\",\"\\\\neg p\",\"\\\\neg q\"]", "description": "", "templateType": "anything", "can_override": false}, "s": {"name": "s", "group": "Lists of symbols", "definition": "repeat(random(0..3),4)", "description": "", "templateType": "anything", "can_override": false}, "ev1": {"name": "ev1", "group": "First Bracket", "definition": "bool_to_label(pre_ev1)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "First Bracket", "definition": "latex(latex_symbol_list[s[0]])", "description": "", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Truth values", "definition": "[true,true,false,false]", "description": "", "templateType": "anything", "can_override": false}, "logic_symbol_list": {"name": "logic_symbol_list", "group": "Lists of symbols", "definition": "[\"p\",\"q\",\"not p\",\"not q\"]", "description": "", "templateType": "anything", "can_override": false}, "pre_ev1": {"name": "pre_ev1", "group": "First Bracket", "definition": "map(evaluate(convch(a)+\" \"+conv(op)+\" \"+convch(b),[p[t],q[t]]),t,0..3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "150"}, "ungrouped_variables": [], "variable_groups": [{"name": "Lists of symbols", "variables": ["logic_symbol_list", "latex_symbol_list", "s"]}, {"name": "First Bracket", "variables": ["a", "b", "op", "pre_ev1", "ev1"]}, {"name": "Second Bracket", "variables": []}, {"name": "Truth values", "variables": ["q", "p", "disp", "disq"]}], "functions": {"convch": {"parameters": [["ch", "string"]], "type": "string", "language": "jme", "definition": "switch(ch=\"\\\\neg p\",\"not p[t]\",ch=\"\\\\neg q\",\"not q[t]\",ch=\"p\",\"p[t]\",\"q[t]\")"}, "evaluate": {"parameters": [["expr", "string"], ["dependencies", "list"]], "type": "number", "language": "javascript", "definition": "return scope.evaluate(expr);"}, "conv": {"parameters": [["op", "string"]], "type": "string", "language": "jme", "definition": "switch(op=\"\\\\land\",\"and\",op=\"\\\\lor\",\"or\",\"implies\")"}, "bool_to_label": {"parameters": [["l", "list"]], "type": "number", "language": "jme", "definition": "map(if(l[x],'T','F'),x,0..length(l)-1)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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": "<p>Complete the following truth table:</p>\n<table border=\"1\">\n<tbody>\n<tr><th>$p$</th><th>$q$</th><th>$\\var{a} \\var{op} \\var{b}$</th></tr>\n<tr>\n<td>$\\var{disp[0]}$</td>\n<td>$\\var{disq[0]}$</td>\n<td>[[0]]</td>\n</tr>\n<tr>\n<td>$\\var{disp[1]}$</td>\n<td>$\\var{disq[1]}$</td>\n<td>[[1]]</td>\n</tr>\n<tr>\n<td>$\\var{disp[2]}$</td>\n<td>$\\var{disq[2]}$</td>\n<td>[[2]]</td>\n</tr>\n<tr>\n<td>$\\var{disp[3]}$</td>\n<td>$\\var{disq[3]}$</td>\n<td>[[3]]</td>\n</tr>\n</tbody>\n</table>", "gaps": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ev1[0]}", "displayAnswer": "{ev1[0]}", "matchMode": "regex"}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ev1[1]}", "displayAnswer": "{ev1[1]}", "matchMode": "regex"}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ev1[2]}", "displayAnswer": "{ev1[2]}", "matchMode": "regex"}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ev1[3]}", "displayAnswer": "{ev1[3]}", "matchMode": "regex"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Truth tables 1(v2)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "variable_groups": [{"variables": ["logic_symbol_list", "latex_symbol_list", "s"], "name": "Lists of symbols"}, {"variables": ["a", "b", "op", "pre_ev1", "ev1"], "name": "First Bracket"}, {"variables": ["a1", "b1", "op2", "pre_ev2", "ev2"], "name": "Second Bracket"}, {"variables": ["p", "q", "disp", "disq"], "name": "Truth values"}], "variables": {"disp": {"templateType": "anything", "group": "Truth values", "definition": "bool_to_label(p)", "description": "", "name": "disp"}, "q": {"templateType": "anything", "group": "Truth values", "definition": "[true,false,true,false]", "description": "", "name": "q"}, "p": {"templateType": "anything", "group": "Truth values", "definition": "[true,true,false,false]", "description": "", "name": "p"}, "b": {"templateType": "anything", "group": "First Bracket", "definition": "latex(latex_symbol_list[s[1]])", "description": "", "name": "b"}, "op": {"templateType": "anything", "group": "First Bracket", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "description": "", "name": "op"}, "latex_symbol_list": {"templateType": "anything", "group": "Lists of symbols", "definition": "[\"p\",\"q\",\"\\\\neg p\",\"\\\\neg q\"]", "description": "", "name": "latex_symbol_list"}, "b1": {"templateType": "anything", "group": "Second Bracket", "definition": "latex(latex_symbol_list[s[3]])", "description": "", "name": "b1"}, "a1": {"templateType": "anything", "group": "Second Bracket", "definition": "latex(latex_symbol_list[s[2]])", "description": "", "name": "a1"}, "op2": {"templateType": "anything", "group": "Second Bracket", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "description": "", "name": "op2"}, "op1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "description": "", "name": "op1"}, "disq": {"templateType": "anything", "group": "Truth values", "definition": "bool_to_label(q)", "description": "", "name": "disq"}, "pre_ev2": {"templateType": "anything", "group": "Second Bracket", "definition": "map(evaluate(convch(a1)+\" \"+conv(op2)+\" \"+convch(b1),[p[t],q[t]]),t,0..3)", "description": "", "name": "pre_ev2"}, "s": {"templateType": "anything", "group": "Lists of symbols", "definition": "repeat(random(0..3),4)", "description": "", "name": "s"}, "ev1": {"templateType": "anything", "group": "First Bracket", "definition": "bool_to_label(pre_ev1)", "description": "", "name": "ev1"}, "a": {"templateType": "anything", "group": "First Bracket", "definition": "latex(latex_symbol_list[s[0]])", "description": "", "name": "a"}, "t_value": {"templateType": "anything", "group": "Ungrouped variables", "definition": "bool_to_label(map(evaluate(pre_ev1[t]+\" \"+conv(op1)+\" \"+pre_ev2[t],[]),t,0..3))", "description": "", "name": "t_value"}, "pre_ev1": {"templateType": "anything", "group": "First Bracket", "definition": "map(evaluate(convch(a)+\" \"+conv(op)+\" \"+convch(b),[p[t],q[t]]),t,0..3)", "description": "", "name": "pre_ev1"}, "logic_symbol_list": {"templateType": "anything", "group": "Lists of symbols", "definition": "[\"p\",\"q\",\"not p\",\"not q\"]", "description": "", "name": "logic_symbol_list"}, "ev2": {"templateType": "anything", "group": "Second Bracket", "definition": "bool_to_label(pre_ev2)", "description": "", "name": "ev2"}}, "ungrouped_variables": ["op1", "t_value"], "rulesets": {}, "showQuestionGroupNames": false, "functions": {"convch": {"type": "string", "language": "jme", "definition": "switch(ch=\"\\\\neg p\",\"not p[t]\",ch=\"\\\\neg q\",\"not q[t]\",ch=\"p\",\"p[t]\",\"q[t]\")", "parameters": [["ch", "string"]]}, "evaluate": {"type": "number", "language": "javascript", "definition": "return scope.evaluate(expr);", "parameters": [["expr", "string"], ["dependencies", "list"]]}, "conv": {"type": "string", "language": "jme", "definition": "switch(op=\"\\\\land\",\"and\",op=\"\\\\lor\",\"or\",\"implies\")", "parameters": [["op", "string"]]}, "bool_to_label": {"type": "number", "language": "jme", "definition": "map(if(l[x],'T','F'),x,0..length(l)-1)", "parameters": [["l", "list"]]}}, "parts": [{"showCorrectAnswer": true, "scripts": {}, "gaps": [{"answer": "{ev1[0]}", "displayAnswer": "{ev1[0]}", "scripts": {}, "type": "patternmatch", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1}, {"answer": "{ev1[1]}", "displayAnswer": "{ev1[1]}", "scripts": {}, "type": "patternmatch", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1}, {"answer": "{ev1[2]}", "displayAnswer": "{ev1[2]}", "scripts": {}, "type": "patternmatch", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1}, {"answer": "{ev1[3]}", "displayAnswer": "{ev1[3]}", "scripts": {}, "type": "patternmatch", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1}, {"answer": "{ev2[0]}", "displayAnswer": "{ev2[0]}", "scripts": {}, "type": "patternmatch", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1}, {"answer": "{ev2[1]}", "displayAnswer": "{ev2[1]}", "scripts": {}, "type": "patternmatch", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1}, {"answer": "{ev2[2]}", "displayAnswer": "{ev2[2]}", "scripts": {}, "type": "patternmatch", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1}, {"answer": "{ev2[3]}", "displayAnswer": "{ev2[3]}", "scripts": {}, "type": "patternmatch", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1}, {"answer": "{t_value[0]}", "displayAnswer": "{t_value[0]}", "scripts": {}, "type": "patternmatch", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1}, {"answer": "{t_value[1]}", "displayAnswer": "{t_value[1]}", "scripts": {}, "type": "patternmatch", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1}, {"answer": "{t_value[2]}", "displayAnswer": "{t_value[2]}", "scripts": {}, "type": "patternmatch", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1}, {"answer": "{t_value[3]}", "displayAnswer": "{t_value[3]}", "scripts": {}, "type": "patternmatch", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "<p>Complete the following truth table:</p>\n<table border=\"1\">\n<tbody>\n<tr><th>$p$</th><th>$q$</th><th>$\\var{a} \\var{op} \\var{b}$</th><th>$\\var{a1} \\var{op2} \\var{b1}$</th><th>$(\\var{a} \\var{op} \\var{b}) \\var{op1} (\\var{a1} \\var{op2} \\var{b1})$</th></tr>\n<tr>\n<td>$\\var{disp[0]}$</td>\n<td>$\\var{disq[0]}$</td>\n<td>[[0]]</td>\n<td>[[4]]</td>\n<td>[[8]]</td>\n</tr>\n<tr>\n<td>$\\var{disp[1]}$</td>\n<td>$\\var{disq[1]}$</td>\n<td>[[1]]</td>\n<td>[[5]]</td>\n<td>[[9]]</td>\n</tr>\n<tr>\n<td>$\\var{disp[2]}$</td>\n<td>$\\var{disq[2]}$</td>\n<td>[[2]]</td>\n<td>[[6]]</td>\n<td>[[10]]</td>\n</tr>\n<tr>\n<td>$\\var{disp[3]}$</td>\n<td>$\\var{disq[3]}$</td>\n<td>[[3]]</td>\n<td>[[7]]</td>\n<td>[[11]]</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "marks": 0}], "variablesTest": {"condition": "a1 <>b1 and\nif(a='p' or a='\\\\neg p',b=random('q','\\\\neg q'),b=random('p','\\\\neg p'))\n", "maxRuns": "150"}, "statement": "<p>In the following question you are asked to construct a truth table for:</p>\n<p>\\[(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1}).\\]</p>\n<p></p>\n<p>Enter T&nbsp;if true, else enter F.</p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>", "tags": [], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Create a truth table for a logical expression of the form $(a \\operatorname{op1} b) \\operatorname{op2}(c \\operatorname{op3} d)$ where $a, \\;b,\\;c,\\;d$ can be the Boolean variables $p,\\;q,\\;\\neg p,\\;\\neg q$ and each of $\\operatorname{op1},\\;\\operatorname{op2},\\;\\operatorname{op3}$ one of $\\lor,\\;\\land,\\;\\to$.</p>\n<p>For example: $(p \\lor \\neg q) \\land(q \\to \\neg p)$.</p>"}, "advice": "<p>First we find the truth table for $\\var{a} \\var{op} \\var{b}$:</p>\n<table border=\"1\">\n<tbody>\n<tr><th>$p$</th><th>$q$</th><th>$\\var{a} \\var{op} \\var{b}$</th></tr>\n<tr>\n<td>$\\var{disp[0]}$</td>\n<td>$\\var{disq[0]}$</td>\n<td>$\\var{ev1[0]}$</td>\n</tr>\n<tr>\n<td>$\\var{disp[1]}$</td>\n<td>$\\var{disq[1]}$</td>\n<td>$\\var{ev1[1]}$</td>\n</tr>\n<tr>\n<td>$\\var{disp[2]}$</td>\n<td>$\\var{disq[2]}$</td>\n<td>$\\var{ev1[2]}$</td>\n</tr>\n<tr>\n<td>$\\var{disp[3]}$</td>\n<td>$\\var{disq[3]}$</td>\n<td>$\\var{ev1[3]}$</td>\n</tr>\n</tbody>\n</table>\n<p>Then the truth table for $\\var{a1} \\var{op2} \\var{b1}$:</p>\n<table border=\"1\">\n<tbody>\n<tr><th>$p$</th><th>$q$</th><th>$\\var{a1} \\var{op2} \\var{b1}$</th></tr>\n<tr>\n<td>$\\var{disp[0]}$</td>\n<td>$\\var{disq[0]}$</td>\n<td>$\\var{ev2[0]}$</td>\n</tr>\n<tr>\n<td>$\\var{disp[1]}$</td>\n<td>$\\var{disq[1]}$</td>\n<td>$\\var{ev2[1]}$</td>\n</tr>\n<tr>\n<td>$\\var{disp[2]}$</td>\n<td>$\\var{disq[2]}$</td>\n<td>$\\var{ev2[2]}$</td>\n</tr>\n<tr>\n<td>$\\var{disp[3]}$</td>\n<td>$\\var{disq[3]}$</td>\n<td>$\\var{ev2[3]}$</td>\n</tr>\n</tbody>\n</table>\n<p>Putting these together to find $(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1})$:</p>\n<p></p>\n<table border=\"1\">\n<tbody>\n<tr><th>$\\var{a} \\var{op} \\var{b}$</th><th>$\\var{a1} \\var{op2} \\var{b1}$</th><th>$(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1})$</th></tr>\n<tr>\n<td>$\\var{ev1[0]}$</td>\n<td>$\\var{ev2[0]}$</td>\n<td>$\\var{t_value[0]}$</td>\n</tr>\n<tr>\n<td>$\\var{ev1[1]}$</td>\n<td>$\\var{ev2[1]}$</td>\n<td>$\\var{t_value[1]}$</td>\n</tr>\n<tr>\n<td>$\\var{ev1[2]}$</td>\n<td>$\\var{ev2[2]}$</td>\n<td>$\\var{t_value[2]}$</td>\n</tr>\n<tr>\n<td>$\\var{ev1[3]}$</td>\n<td>$\\var{ev2[3]}$</td>\n<td>$\\var{t_value[3]}$</td>\n</tr>\n</tbody>\n</table>"}, {"name": "Truth tables 2 (v2) -", "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/"}], "variablesTest": {"condition": "a1 <>b1  and\nif(a='p' or a='\\\\neg p',b=random('q','\\\\neg q'),b=random('p','\\\\neg p'))\n", "maxRuns": "150"}, "variables": {"a": {"templateType": "anything", "group": "First Bracket", "definition": "latex(latex_symbol_list[s[0]])", "description": "", "name": "a"}, "op": {"templateType": "anything", "group": "First Bracket", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "description": "", "name": "op"}, "op4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "description": "", "name": "op4"}, "a1": {"templateType": "anything", "group": "Second Bracket", "definition": "latex(latex_symbol_list[s[2]])", "description": "", "name": "a1"}, "op2": {"templateType": "anything", "group": "Second Bracket", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "description": "", "name": "op2"}, "op1": {"templateType": "anything", "group": "First and Second Brackets", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "description": "", "name": "op1"}, "ev1": {"templateType": "anything", "group": "First Bracket", "definition": "bool_to_label(pre_ev1)", "description": "", "name": "ev1"}, "b": {"templateType": "anything", "group": "First Bracket", "definition": "latex(latex_symbol_list[s[1]])", "description": "", "name": "b"}, "ev3": {"templateType": "anything", "group": "Last ", "definition": "bool_to_label(pre_ev3)", "description": "", "name": "ev3"}, "p": {"templateType": "anything", "group": "Truth values", "definition": "bool_to_label([true,true,false,false])", "description": "", "name": "p"}, "a2": {"templateType": "anything", "group": "Last ", "definition": "latex(random(\"\\\\neg p\",\"\\\\neg q\"))", "description": "", "name": "a2"}, "bool_p": {"templateType": "anything", "group": "Truth values", "definition": "[true,true,false,false]", "description": "", "name": "bool_p"}, "logic_symbol_list": {"templateType": "anything", "group": "Lists of symbols", "definition": "[\"p\",\"q\",\"not 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"latex(latex_symbol_list[s[3]])", "description": "", "name": "b1"}, "pre_ev2": {"templateType": "anything", "group": "Second Bracket", "definition": "map(evaluate(convch(a1)+\" \"+conv(op2)+\" \"+convch(b1),[bool_p[t],bool_q[t]]),t,0..3)", "description": "", "name": "pre_ev2"}, "pre_final_value": {"templateType": "anything", "group": "Ungrouped variables", "definition": "map(evaluate(pre_t_value[t]+\" \"+conv(op4)+\" \"+pre_ev3[t],[]),t,0..3)", "description": "", "name": "pre_final_value"}, "final_value": {"templateType": "anything", "group": "Ungrouped variables", "definition": "bool_to_label(pre_final_value)", "description": "", "name": "final_value"}, "s": {"templateType": "anything", "group": "Lists of symbols", "definition": "repeat(random(0..3),6)", "description": "", "name": "s"}, "bool_q": {"templateType": "anything", "group": "Truth values", "definition": "[true,false,true,false]", "description": "", "name": "bool_q"}, "t_value": {"templateType": "anything", "group": "First and Second Brackets", "definition": "bool_to_label(pre_t_value)", "description": "", "name": "t_value"}, "pre_t_value": {"templateType": "anything", "group": "First and Second Brackets", "definition": "map(evaluate(pre_ev1[t]+\" \"+conv(op1)+\" \"+pre_ev2[t],[]),t,0..3)", "description": "", "name": "pre_t_value"}}, "ungrouped_variables": ["pre_final_value", "op4", "final_value"], "preamble": {"css": "", "js": ""}, "functions": {"evaluate": {"type": "number", "language": "javascript", "definition": "return scope.evaluate(expr);", "parameters": [["expr", "string"], ["dependencies", "list"]]}, "convch": {"type": "string", "language": "jme", "definition": "switch(ch=\"\\\\neg p\",\"not bool_p[t]\",ch=\"\\\\neg q\",\"not bool_q[t]\",ch=\"p\",\"bool_p[t]\",\"bool_q[t]\")", "parameters": [["ch", "string"]]}, "conv": {"type": "string", "language": "jme", "definition": "switch(op=\"\\\\land\",\"and\",op=\"\\\\lor\",\"or\",\"implies\")", "parameters": [["op", "string"]]}, "bool_to_label": {"type": "number", "language": "jme", "definition": "map(if(l[x],'T','F'),x,0..length(l)-1)", "parameters": [["l", "list"]]}}, "variable_groups": [{"variables": ["logic_symbol_list", "latex_symbol_list", "s"], "name": "Lists of symbols"}, {"variables": ["a", "b", "op", "pre_ev1", "ev1"], "name": "First Bracket"}, {"variables": ["a1", "b1", "op2", "pre_ev2", "ev2"], "name": "Second Bracket"}, {"variables": ["p", "q", "bool_p", "bool_q"], "name": "Truth values"}, {"variables": ["a2", "pre_ev3", "ev3"], "name": "Last "}, {"variables": ["op1", "pre_t_value", "t_value"], "name": "First and Second Brackets"}], "parts": [{"customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "<p>Complete the following truth table:</p>\n<table border=\"1\">\n<tbody>\n<tr><th>$p$</th><th>$q$</th><th>$\\var{a} \\var{op} \\var{b}$</th><th>$\\var{a1} \\var{op2} \\var{b1}$</th><th>$(\\var{a} \\var{op} \\var{b}) \\var{op1} (\\var{a1} \\var{op2} \\var{b1})$</th><th>$\\var{a2} $</th><th>$((\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1}))\\var{op4}\\var{a2} $</th></tr>\n<tr>\n<td>$\\var{p[0]}$</td>\n<td>$\\var{q[0]}$</td>\n<td>[[0]]</td>\n<td>[[4]]</td>\n<td>[[8]]</td>\n<td>[[12]]</td>\n<td>[[16]]</td>\n</tr>\n<tr>\n<td>$\\var{p[1]}$</td>\n<td>$\\var{q[1]}$</td>\n<td>[[1]]</td>\n<td>[[5]]</td>\n<td>[[9]]</td>\n<td>[[13]]</td>\n<td>[[17]]</td>\n</tr>\n<tr>\n<td>$\\var{p[2]}$</td>\n<td>$\\var{q[2]}$</td>\n<td>[[2]]</td>\n<td>[[6]]</td>\n<td>[[10]]</td>\n<td>[[14]]</td>\n<td>[[18]]</td>\n</tr>\n<tr>\n<td>$\\var{p[3]}$</td>\n<td>$\\var{q[3]}$</td>\n<td>[[3]]</td>\n<td>[[7]]</td>\n<td>[[11]]</td>\n<td>[[15]]</td>\n<td>[[19]]</td>\n</tr>\n</tbody>\n</table>", "unitTests": [], "sortAnswers": false, "scripts": {}, "gaps": [{"answer": "{ev1[0]}", "displayAnswer": "{ev1[0]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{ev1[1]}", "displayAnswer": "{ev1[1]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{ev1[2]}", "displayAnswer": "{ev1[2]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{ev1[3]}", "displayAnswer": "{ev1[3]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": 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"scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{ev2[3]}", "displayAnswer": "{ev2[3]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{t_value[0]}", "displayAnswer": "{t_value[0]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{t_value[1]}", "displayAnswer": "{t_value[1]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{t_value[2]}", "displayAnswer": "{t_value[2]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{t_value[3]}", "displayAnswer": "{t_value[3]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{ev3[0]}", "displayAnswer": "{ev3[0]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{ev3[1]}", "displayAnswer": "{ev3[1]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{ev3[2]}", "displayAnswer": "{ev3[2]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{ev3[3]}", "displayAnswer": "{ev3[3]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{final_value[0]}", "displayAnswer": "{final_value[0]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{final_value[1]}", "displayAnswer": "{final_value[1]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{final_value[2]}", "displayAnswer": "{final_value[2]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"answer": "{final_value[3]}", "displayAnswer": "{final_value[3]}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}], "statement": "<p>In the following question you are asked to construct a truth table for:</p>\n<p>\\[((\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1}))\\var{op4}\\var{a2}.\\]</p>\n<p></p>\n<p>Enter T&nbsp;if true, else enter F.</p>", "tags": [], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Create a truth table for a logical expression of the form $((a \\operatorname{op1} b) \\operatorname{op2}(c \\operatorname{op3} d))\\operatorname{op4}e $ where each of $a, \\;b,\\;c,\\;d,\\;e$ can be one the Boolean variables $p,\\;q,\\;\\neg p,\\;\\neg q$ and each of $\\operatorname{op1},\\;\\operatorname{op2},\\;\\operatorname{op3},\\;\\operatorname{op4}$ one of $\\lor,\\;\\land,\\;\\to$.</p>\n<p>For example: $((q \\lor \\neg p) \\to (p \\land \\neg q)) \\lor \\neg q$</p>"}, "type": "question", "advice": "<p>First we find the truth table for $\\var{a} \\var{op} \\var{b}$:</p>\n<table border=\"1\">\n<tbody>\n<tr><th>$p$</th><th>$q$</th><th>$\\var{a} \\var{op} \\var{b}$</th></tr>\n<tr>\n<td>$\\var{p[0]}$</td>\n<td>$\\var{q[0]}$</td>\n\n<td>$\\var{ev1[0]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[1]}$</td>\n<td>$\\var{q[1]}$</td>\n\n<td>$\\var{ev1[1]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[2]}$</td>\n<td>$\\var{q[2]}$</td>\n\n<td>$\\var{ev1[2]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[3]}$</td>\n<td>$\\var{q[3]}$</td>\n\n<td>$\\var{ev1[3]}$</td>\n</tr>\n</tbody>\n</table>\n<p>Then the truth table for $\\var{a1} \\var{op2} \\var{b1}$:</p>\n<table border=\"1\">\n<tbody>\n<tr><th>$p$</th><th>$q$</th><th>$\\var{a1} \\var{op2} \\var{b1}$</th></tr>\n<tr>\n<td>$\\var{p[0]}$</td>\n<td>$\\var{q[0]}$</td>\n<td>$\\var{ev2[0]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[1]}$</td>\n<td>$\\var{q[1]}$</td>\n<td>$\\var{ev2[1]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[2]}$</td>\n<td>$\\var{q[2]}$</td>\n<td>$\\var{ev2[2]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[3]}$</td>\n<td>$\\var{q[3]}$</td>\n<td>$\\var{ev2[3]}$</td>\n</tr>\n</tbody>\n</table>\n<p>Putting these together to find $(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1})$:</p>\n<p></p>\n<table border=\"1\">\n<tbody>\n<tr><th>$p$</th><th>$q$</th><th>$\\var{a} \\var{op} \\var{b}$</th><th>$\\var{a1} \\var{op2} \\var{b1}$</th><th>$(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1})$</th></tr>\n<tr>\n<td>$\\var{p[0]}$</td>\n<td>$\\var{q[0]}$</td>\n<td>$\\var{ev1[0]}$</td>\n<td>$\\var{ev2[0]}$</td>\n<td>$\\var{t_value[0]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[1]}$</td>\n<td>$\\var{q[1]}$</td>\n<td>$\\var{ev1[1]}$</td>\n<td>$\\var{ev2[1]}$</td>\n<td>$\\var{t_value[1]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[2]}$</td>\n<td>$\\var{q[2]}$</td>\n<td>$\\var{ev1[2]}$</td>\n<td>$\\var{ev2[2]}$</td>\n<td>$\\var{t_value[2]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[3]}$</td>\n<td>$\\var{q[3]}$</td>\n<td>$\\var{ev1[3]}$</td>\n<td>$\\var{ev2[3]}$</td>\n<td>$\\var{t_value[3]}$</td>\n</tr>\n</tbody>\n</table>\n<p>Next we find the truth table for $\\var{a2}$:</p>\n<table border=\"1\">\n<tbody>\n<tr><th>$p$</th><th>$q$</th><th>$\\var{a2}$</th></tr>\n<tr>\n<td>$\\var{p[0]}$</td>\n<td>$\\var{q[0]}$</td>\n<td>$\\var{ev3[0]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[1]}$</td>\n<td>$\\var{q[1]}$</td>\n<td>$\\var{ev3[1]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[2]}$</td>\n<td>$\\var{q[2]}$</td>\n<td>$\\var{ev3[2]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[3]}$</td>\n<td>$\\var{q[3]}$</td>\n<td>$\\var{ev3[3]}$</td>\n</tr>\n</tbody>\n</table>\n<p>Putting this all together to obtain the truth table we want:</p>\n<table border=\"1\">\n<tbody>\n<tr><th>$p$</th><th>$q$</th><th>$(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1})$</th><th>$\\var{a2}$</th><th>$((\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1}))\\var{op4}\\var{a2} $</th></tr>\n<tr>\n<td>$\\var{p[0]}$</td>\n<td>$\\var{q[0]}$</td>\n<td>$\\var{t_value[0]}$</td>\n<td>$\\var{ev3[0]}$</td>\n<td>$\\var{final_value[0]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[1]}$</td>\n<td>$\\var{q[1]}$</td>\n<td>$\\var{t_value[1]}$</td>\n<td>$\\var{ev3[1]}$</td>\n<td>$\\var{final_value[1]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[2]}$</td>\n<td>$\\var{q[2]}$</td>\n<td>$\\var{t_value[2]}$</td>\n<td>$\\var{ev3[2]}$</td>\n<td>$\\var{final_value[2]}$</td>\n</tr>\n<tr>\n<td>$\\var{p[3]}$</td>\n<td>$\\var{q[3]}$</td>\n<td>$\\var{t_value[3]}$</td>\n<td>$\\var{ev3[3]}$</td>\n<td>$\\var{final_value[3]}$</td>\n</tr>\n</tbody>\n</table>"}]}], "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": 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