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{"name": "Lois's copy of Basic Set Theory: set operations", "extensions": [], "custom_part_types": [], "resources": [["question-resources/384px-Venn0111.svg.png", "/srv/numbas/media/question-resources/384px-Venn0111.svg.png"], ["question-resources/384px-Venn0001.svg.png", "/srv/numbas/media/question-resources/384px-Venn0001.svg.png"], ["question-resources/384px-Venn0110.svg.png", "/srv/numbas/media/question-resources/384px-Venn0110.svg.png"], ["question-resources/240px-Venn0100.svg.png", "/srv/numbas/media/question-resources/240px-Venn0100.svg.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"css": "", "js": ""}, "variable_groups": [], "tags": [], "variablesTest": {"condition": "not(listA = listB)", "maxRuns": 100}, "variables": {"listB": {"description": "", "group": "Ungrouped variables", "definition": "repeat(random(0..4),4)", "name": "listB", "templateType": "anything"}, "listA": {"description": "", "group": "Ungrouped variables", "definition": "repeat(random(5..9),4)", "name": "listA", "templateType": "anything"}, "listN": {"description": "", "group": "Ungrouped variables", "definition": "repeat(random(1..9),2)", "name": "listN", "templateType": "anything"}, "B": {"description": "", "group": "Ungrouped variables", "definition": "union(set(listB),set(listN))", "name": "B", "templateType": "anything"}, "A": {"description": "", "group": "Ungrouped variables", "definition": "union(set(listA),set(listN))", "name": "A", "templateType": "anything"}}, "ungrouped_variables": ["listA", "listB", "A", "B", "listN"], "advice": "<p>The union of two sets is the set of elements from either set</p>\n<p style=\"text-align: center;\">$ A \\cup B = \\left\\{ x\\, |\\, x \\in A \\text{ or } x \\in B\\right\\}$</p>\n<hr/>\n<p style=\"text-align: left;\">The intersetction of two sets is the set of elements common to both sets</p>\n<p style=\"text-align: center;\">$ A \\cap B = \\left\\{ x\\, |\\, x \\in A \\text{ and } x \\in B\\right\\}$</p>\n<hr/>\n<p style=\"text-align: left;\">The difference $A-B$ is the set of elements from $A$ which are not in $B$:</p>\n<p style=\"text-align: center;\">$ A - B = \\left\\{ x \\in A |\\, x \\notin B\\right\\}$</p>\n<hr/>\n<p style=\"text-align: left;\">Similarly, the difference $B-A$ is the set of elements from $B$ which are not in $A$:</p>\n<p style=\"text-align: center;\">$ B - A = \\left\\{ x \\in B |\\, x \\notin A\\right\\}$</p>\n<hr/>\n<p style=\"text-align: left;\">The symmetric difference $A \\Delta B$ is the union of the set differences, but it can also be expressed as the union minus the intersection</p>\n<p style=\"text-align: center;\">$ A \\Delta B = (A \\cup B) - (A \\cap B)$.</p>", "metadata": {"licence": "Creative Commons Attribution-ShareAlike 4.0 International", "description": "<p>Simple exercises introducing the fundamental set operations, and NUMBAS syntax for sets.</p>"}, "statement": "<p>Consider the sets &nbsp;and B = ${B}$. Find the union, intersection and set differences below. Use the NUMBAS syntax <code>set(1,2,3)</code> for $\\left\\{1,2,3\\right\\}$.</p>", "extensions": [], "rulesets": {}, "parts": [{"marks": 1, "type": "jme", "checkingtype": "absdiff", "showpreview": true, "showCorrectAnswer": true, "expectedvariablenames": [], "prompt": "<p>What is the union $A \\cup B$?</p>", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "scripts": {"validate": {"order": "instead", "script": "try {\n  var tree = Numbas.jme.compile(this.studentAnswer);\n  var type = Numbas.jme.evaluate(tree,this.question.scope).type;\n  \n  if ('set' != type) { \n    this.giveWarning(\"Your answer must be a set. Use the syntax set(1,2,3) for the set $\\\\left\\\\{1,2,3\\\\right\\\\}$\");\n    return false;\n  }\n  \n  return true;\n}\ncatch(e) {\n  this.markingComment(e);\n  return false;\n}"}}, "answer": "{union(A,B)}", "vsetrangepoints": 5, "variableReplacements": [], "vsetrange": [0, 1], "checkingaccuracy": 0.001}, {"marks": 1, "type": "jme", "checkingtype": "absdiff", "showpreview": true, "showCorrectAnswer": true, "expectedvariablenames": [], "prompt": "<p>What is the intersection $A \\cap B$?</p>", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "scripts": {"validate": {"order": "instead", "script": "try {\n  var tree = Numbas.jme.compile(this.studentAnswer);\n  var type = Numbas.jme.evaluate(tree,this.question.scope).type;\n  \n  if ('set' != type) { \n    this.giveWarning(\"Your answer must be a set. Use the syntax set(1,2,3) for the set $\\\\left\\\\{1,2,3\\\\right\\\\}$\");\n    return false;\n  }\n  \n  return true;\n}\ncatch(e) {\n  this.markingComment(e);\n  return false;\n}"}}, "answer": "{intersection(A,B)}", "vsetrangepoints": 5, "variableReplacements": [], "vsetrange": [0, 1], "checkingaccuracy": 0.001}, {"marks": 1, "type": "jme", "checkingtype": "absdiff", "showpreview": true, "showCorrectAnswer": true, "expectedvariablenames": [], "prompt": "<p>What is $A-B$, the set of elements from $A$ which are not in $B$?</p>", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "scripts": {"validate": {"order": "instead", "script": "try {\n  var tree = Numbas.jme.compile(this.studentAnswer);\n  var type = Numbas.jme.evaluate(tree,this.question.scope).type;\n  \n  if ('set' != type) { \n    this.giveWarning(\"Your answer must be a set. Use the syntax set(1,2,3) for the set $\\\\left\\\\{1,2,3\\\\right\\\\}$\");\n    return false;\n  }\n  \n  return true;\n}\ncatch(e) {\n  this.markingComment(e);\n  return false;\n}"}}, "answer": "{A-B}", "vsetrangepoints": 5, "variableReplacements": [], "vsetrange": [0, 1], "checkingaccuracy": 0.001}, {"marks": 1, "type": "jme", "checkingtype": "absdiff", "showpreview": true, "showCorrectAnswer": true, "expectedvariablenames": [], "prompt": "<p>What is $B-A$, the set of elements from $B$ which are not in $A$?</p>", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "scripts": {"validate": {"order": "instead", "script": "try {\n  var tree = Numbas.jme.compile(this.studentAnswer);\n  var type = Numbas.jme.evaluate(tree,this.question.scope).type;\n  \n  if ('set' != type) { \n    this.giveWarning(\"Your answer must be a set. Use the syntax set(1,2,3) for the set $\\\\left\\\\{1,2,3\\\\right\\\\}$\");\n    return false;\n  }\n  \n  return true;\n}\ncatch(e) {\n  this.markingComment(e);\n  return false;\n}"}}, "answer": "{B-A}", "vsetrangepoints": 5, "variableReplacements": [], "vsetrange": [0, 1], "checkingaccuracy": 0.001}, {"marks": 1, "type": "jme", "checkingtype": "absdiff", "showpreview": true, "showCorrectAnswer": true, "expectedvariablenames": [], "prompt": "<p>What is union of the set differences $(A-B)\\cup(B-A)$? This is also called the <strong>symmetric difference</strong> $A\\Delta B$.</p>", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "scripts": {"validate": {"order": "instead", "script": "try {\n  var tree = Numbas.jme.compile(this.studentAnswer);\n  var type = Numbas.jme.evaluate(tree,this.question.scope).type;\n  \n  if ('set' != type) { \n    this.giveWarning(\"Your answer must be a set. Use the syntax set(1,2,3) for the set $\\\\left\\\\{1,2,3\\\\right\\\\}$\");\n    return false;\n  }\n  \n  return true;\n}\ncatch(e) {\n  this.markingComment(e);\n  return false;\n}"}}, "answer": "{union(A-B,B-A)}", "vsetrangepoints": 5, "variableReplacements": [], "vsetrange": [0, 1], "checkingaccuracy": 0.001}, {"choices": ["<p>$A\\cup B$</p>", "<p>$A \\cap B$</p>", "<p>$A \\Delta B$</p>", "<p>$A - B$</p>"], "warningType": "none", "marks": 0, "type": "m_n_x", "shuffleChoices": true, "scripts": {}, "showCorrectAnswer": true, "displayType": "radiogroup", "matrix": [["0.25", 0, 0, 0], [0, "0.25", 0, 0], [0, 0, "0.25", 0], [0, 0, 0, "0.25"]], "prompt": "<p>Match the mathematical expression with its Venn diagram.</p>\n<p></p>", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "maxMarks": "1", "layout": {"expression": "", "type": "all"}, "minMarks": 0, "variableReplacements": [], "minAnswers": 0, "answers": ["<p><img src=\"resources/question-resources/384px-Venn0111.svg.png\" width=\"200\" height=\"146\" /></p>", "<p><img src=\"resources/question-resources/384px-Venn0001.svg.png\" width=\"200\" height=\"146\" /></p>", "<p><img src=\"resources/question-resources/384px-Venn0110.svg.png\" width=\"200\" height=\"146\" /></p>", "<p><img src=\"resources/question-resources/240px-Venn0100.svg.png\" width=\"200\" height=\"146\" /></p>"], "maxAnswers": 0, "shuffleAnswers": true}], "name": "Lois's copy of Basic Set Theory: set operations", "functions": {}, "type": "question", "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}