// Numbas version: exam_results_page_options {"name": "Shivendra's copy of 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": [{"variable_groups": [], "functions": {}, "variablesTest": {"maxRuns": 100, "condition": "AB + BC + CA =1 and AsubsetB + BsubsetA + AsubsetC + CsubsetA + BsubsetC + CsubsetB=4"}, "variables": {"AB": {"group": "Ungrouped variables", "templateType": "anything", "name": "AB", "definition": "if(set(A) = set(B),1,0)", "description": ""}, "BsubsetC": {"group": "Ungrouped variables", "templateType": "anything", "name": "BsubsetC", "definition": "if(set(B)=intersection(set(C),set(B)),1,0)", "description": ""}, "A": {"group": "Ungrouped variables", "templateType": "anything", "name": "A", "definition": "repeat(random(1..4),4)", "description": ""}, "B": {"group": "Ungrouped variables", "templateType": "anything", "name": "B", "definition": "repeat(random(1..4),5)", "description": ""}, "C": {"group": "Ungrouped variables", "templateType": "anything", "name": "C", "definition": "repeat(random(1..4),6)", "description": ""}, "CA": {"group": "Ungrouped variables", "templateType": "anything", "name": "CA", "definition": "if(set(C) = set(A),1,0)", "description": ""}, "BsubsetA": {"group": "Ungrouped variables", "templateType": "anything", "name": "BsubsetA", "definition": "if(set(B)=intersection(set(A),set(B)),1,0)", "description": ""}, "AsubsetB": {"group": "Ungrouped variables", "templateType": "anything", "name": "AsubsetB", "definition": "if(set(A)=intersection(set(A),set(B)),1,0)", "description": ""}, "CsubsetA": {"group": "Ungrouped variables", "templateType": "anything", "name": "CsubsetA", "definition": "if(set(C)=intersection(set(A),set(C)),1,0)", "description": ""}, "CsubsetB": {"group": "Ungrouped variables", "templateType": "anything", "name": "CsubsetB", "definition": "if(set(C)=intersection(set(C),set(B)),1,0)", "description": ""}, "AsubsetC": {"group": "Ungrouped variables", "templateType": "anything", "name": "AsubsetC", "definition": "if(set(A)=intersection(set(A),set(C)),1,0)", "description": ""}, "BC": {"group": "Ungrouped variables", "templateType": "anything", "name": "BC", "definition": "if(set(B) = set(C),1,0)", "description": ""}}, "extensions": [], "advice": "

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.

\n
\n

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 $x=y$.

", "rulesets": {}, "parts": [{"shuffleChoices": false, "displayColumns": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "minMarks": 0, "distractors": ["", "", "", "", "", ""], "minAnswers": 0, "scripts": {}, "choices": ["

$A \\subseteq B$

", "

$B \\subseteq A$

", "

$C \\subseteq B$

", "

$B \\subseteq C$

", "

$C \\subseteq A$

", "

$A \\subseteq C$

"], "marks": 0, "warningType": "none", "displayType": "checkbox", "variableReplacements": [], "prompt": "

If every element of the set $A$ is also an element of the set $B$ then we say that $A$ is a subset of $B$: $A \\subseteq B$. Which sets are subsets of one another?

", "maxAnswers": 0, "type": "m_n_2", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customName": "", "matrix": ["AsubsetB", "BsubsetA", "CsubsetB", "BsubsetC", "CsubsetA", "AsubsetC"], "useCustomName": false, "maxMarks": 0, "showCellAnswerState": true, "showCorrectAnswer": true, "unitTests": []}, {"shuffleChoices": false, "displayColumns": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "minMarks": 0, "distractors": ["", "", ""], "minAnswers": 0, "scripts": {}, "choices": ["

$A=B$

", "

$B=C$

", "

$C=A$

"], "marks": 0, "warningType": "none", "displayType": "checkbox", "variableReplacements": [], "prompt": "

Sets are equal if they are subsets of each other. Which sets are equal?

", "maxAnswers": 0, "type": "m_n_2", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customName": "", "matrix": ["AB", "BC", "CA"], "useCustomName": false, "maxMarks": 0, "showCellAnswerState": true, "showCorrectAnswer": true, "unitTests": []}, {"mustBeReduced": false, "allowFractions": false, "precision": "2", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "showPrecisionHint": true, "mustBeReducedPC": 0, "scripts": {}, "minValue": "3.14", "marks": "3", "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "prompt": "

pi is 

", "correctAnswerFraction": false, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "customName": "", "maxValue": "3.14", "strictPrecision": false, "useCustomName": false, "precisionType": "dp", "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "unitTests": []}], "metadata": {"licence": "Creative Commons Attribution-ShareAlike 4.0 International", "description": "

Introductory exercise about set equality

"}, "name": "Shivendra's copy of Basic Set Theory: subsets and set equality", "preamble": {"js": "", "css": ""}, "statement": "

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 set $\\left\\{1,1,2\\right\\}$. 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 $\\left\\{1,2\\right\\}$.

\n

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 $C=\\left\\{\\var{C[0]},\\var{C[1]},\\var{C[2]},\\var{C[3]},\\var{C[4]},\\var{C[5]}\\right\\}$.

", "ungrouped_variables": ["A", "B", "C", "AB", "BC", "CA", "AsubsetB", "BsubsetA", "CsubsetB", "BsubsetC", "CsubsetA", "AsubsetC"], "tags": [], "type": "question", "contributors": [{"name": "Daniel Mansfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/743/"}, {"name": "Shivendra Dayal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3002/"}]}]}], "contributors": [{"name": "Daniel Mansfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/743/"}, {"name": "Shivendra Dayal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3002/"}]}