// Numbas version: exam_results_page_options
{"name": "Blathnaid's copy of Union, complement, intersection", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Blathnaid's copy of Union, complement, intersection", "tags": [], "metadata": {"description": "<p>Given some random finite subsets of the natural numbers, perform set operations $\\cap,\\;\\cup$ and complement.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>In this question, the universal set is &nbsp;$\\mathcal{U}=\\{x \\in \\mathbb{N}\\; | \\;x \\leq \\var{a}\\}$.</p>\n<p>Let:</p>\n<p>$A=\\{x \\in \\mathbb{N}\\;|\\;\\var{b}\\leq x \\leq \\var{c}\\}$.</p>\n<p>$B=\\{x \\in \\mathbb{N}\\;|\\;x \\gt \\var{d}\\}$.</p>\n<p>$C=\\{ x \\in \\mathbb{N}\\;|\\; x \\text{ divisible by } \\var{f}\\}$.</p>\n<p></p>\n<p></p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"f": {"name": "f", "group": "Ungrouped variables", "definition": "random(2,3,5,6)", "description": "", "templateType": "anything", "can_override": false}, "universal": {"name": "universal", "group": "Ungrouped variables", "definition": "set(1..a)", "description": "", "templateType": "anything", "can_override": false}, "set3": {"name": "set3", "group": "Ungrouped variables", "definition": "set(mod_set(1,a,f))", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(15..30)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(3..8)", "description": "", "templateType": "anything", "can_override": false}, "set2": {"name": "set2", "group": "Ungrouped variables", "definition": "set(d+1..a)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(5..c-1)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "b+random(10..a-b)", "description": "", "templateType": "anything", "can_override": false}, "set1": {"name": "set1", "group": "Ungrouped variables", "definition": "set(b..c)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "universal", "set1", "set2", "set3"], "variable_groups": [], "functions": {"mod_set": {"parameters": [["a", "number"], ["b", "number"], ["c", "number"]], "type": "list", "language": "javascript", "definition": "//returns all integers which are divisible by c betweeen a and b\nvar l=[];\nfor(var i=a;i<b+1;i++) \n{ if (i%c==0){l.push(i);}\n}\nreturn l;\n"}}, "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>Enumerate the following sets:</p>\n<p>a) $A \\cap B=\\;$[[0]]</p>\n<p></p>\n<p>d) $(\\overline{A} \\cup C) \\cap B=\\;$[[1]]</p>\n<p></p>\n<p>Note that you input sets in the form <code>set(a,b,c,..,z)</code> .</p>\n<p>For example <code> set(1,2,3)</code>gives the set $\\{1,2,3\\}$.</p>\n<p>The empty set is input as&nbsp;<code>set()</code>.</p>\n<p>Also some labour saving tips:</p>\n<p>If you want to input all integers between $a$ and $b$ inclusive then instead of writing all the elements you can input this as <code>set(a..b)</code>.</p>\n<p>If you want to input all integers between $a$ and $b$ inclusive in steps of $c$ then this is input as <code>set(a..b#c)</code>. So all odd integers from $-3$ to $28$ are input as&nbsp;<code>set(-3..28#2).</code></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{set1 and set2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{((universal-set1) or set3) and set2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Peter Chapman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/210/"}, {"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}]}]}], "contributors": [{"name": "Peter Chapman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/210/"}, {"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}]}