// Numbas version: finer_feedback_settings
{"name": "Basic Set Theory: subsets and set equality", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Basic Set Theory: subsets and set equality", "tags": [], "metadata": {"description": "<p>Introductory exercise about set equality</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>Consider the three individual elements $1, 1$ and $2$. If we consider these elements as a single unordered collection of distinct objects then we call it the <strong>set</strong> $\\left\\{1,1,2\\right\\}$. Because sets are unordered this is the same as $\\left\\{2,1,1\\right\\}$ and because we only collect distinct objects this is also the same as $\\left\\{1,2\\right\\}$.</p>\n<p>For example, let $A=\\left\\{\\var{A[0]},\\var{A[1]},\\var{A[2]},\\var{A[3]}\\right\\}, B=\\left\\{\\var{B[0]},\\var{B[1]},\\var{B[2]},\\var{B[3]},\\var{B[4]}\\right\\}$ and $C=\\left\\{\\var{C[0]},\\var{C[1]},\\var{C[2]},\\var{C[3]},\\var{C[4]},\\var{C[5]}\\right\\}$.</p>", "advice": "<p>You can check to see if $A \\subset B$ by progressively checking if each element of $A$ is also in $B$. There are six questions so you will have to do this six times.</p>\n<hr/>\n<p>The second part of this question builds on the first. You just need to look at your answers and find the sets which contain each other. It is a bit like the 'less than or equal to' relation in the sense that if you have two numbers $x$ and $y$ where $x \\leq y$ and $y\\leq x$, then it must be true that $x=y$.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"B": {"name": "B", "group": "Ungrouped variables", "definition": "repeat(random(1..4),5)", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "repeat(random(1..4),4)", "description": "", "templateType": "anything", "can_override": false}, "BsubsetC": {"name": "BsubsetC", "group": "Ungrouped variables", "definition": "if(set(B)=intersection(set(C),set(B)),1,0)", "description": "", "templateType": "anything", "can_override": false}, "BsubsetA": {"name": "BsubsetA", "group": "Ungrouped variables", "definition": "if(set(B)=intersection(set(A),set(B)),1,0)", "description": "", "templateType": "anything", "can_override": false}, "AB": {"name": "AB", "group": "Ungrouped variables", "definition": "if(set(A) = set(B),1,0)", "description": "", "templateType": "anything", "can_override": false}, "AsubsetB": {"name": "AsubsetB", "group": "Ungrouped variables", "definition": "if(set(A)=intersection(set(A),set(B)),1,0)", "description": "", "templateType": "anything", "can_override": false}, "BC": {"name": "BC", "group": "Ungrouped variables", "definition": "if(set(B) = set(C),1,0)", "description": "", "templateType": "anything", "can_override": false}, "CsubsetB": {"name": "CsubsetB", "group": "Ungrouped variables", "definition": "if(set(C)=intersection(set(C),set(B)),1,0)", "description": "", "templateType": "anything", "can_override": false}, "CA": {"name": "CA", "group": "Ungrouped variables", "definition": "if(set(C) = set(A),1,0)", "description": "", "templateType": "anything", "can_override": false}, "CsubsetA": {"name": "CsubsetA", "group": "Ungrouped variables", "definition": "if(set(C)=intersection(set(A),set(C)),1,0)", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "repeat(random(1..4),6)", "description": "", "templateType": "anything", "can_override": false}, "AsubsetC": {"name": "AsubsetC", "group": "Ungrouped variables", "definition": "if(set(A)=intersection(set(A),set(C)),1,0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "AB + BC + CA =1 and AsubsetB + BsubsetA + AsubsetC + CsubsetA + BsubsetC + CsubsetB=4", "maxRuns": 100}, "ungrouped_variables": ["A", "B", "C", "AB", "BC", "CA", "AsubsetB", "BsubsetA", "CsubsetB", "BsubsetC", "CsubsetA", "AsubsetC"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "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>If every element of the set $A$ is also an element of the set $B$ then we say that $A$ is a <strong>subset</strong> of $B$: $A \\subseteq B$. Which sets are subsets of one another?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["<p>$A \\subseteq B$</p>", "<p>$B \\subseteq A$</p>", "<p>$C \\subseteq B$</p>", "<p>$B \\subseteq C$</p>", "<p>$C \\subseteq A$</p>", "<p>$A \\subseteq C$</p>"], "matrix": ["AsubsetB", "BsubsetA", "CsubsetB", "BsubsetC", "CsubsetA", "AsubsetC"], "distractors": ["", "", "", "", "", ""]}, {"type": "m_n_2", "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>Sets are equal if they are subsets of each other. 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