// Numbas version: finer_feedback_settings
{"name": "Set 2-3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"mod_set": {"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", "type": "list", "language": "javascript", "parameters": [["a", "number"], ["b", "number"], ["c", "number"]]}}, "ungrouped_variables": ["a", "b", "c", "d", "f", "universal", "set1", "set2", "set3"], "name": "Set 2-3", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Enumerate the following sets:</p>\n<p>a) $A \\cap B=\\;$[[0]]</p>\n<p>b) $B \\cap C=\\;$[[1]]</p>\n<p>c) $A \\cap C^{c}=\\;$[[2]]</p>\n<p>d) $(A^{c} \\cup C) \\cap B=\\;$[[3]]</p>\n<p>e) $(A \\cup C)^{c} \\cap B^{c}=\\;$[[4]]</p>\n<p>f)&nbsp;$(A \\cup B^{c}) \\cap C=\\;$[[5]]</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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{set1 and set2}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{set2 and set3}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{set1 and (universal-set3)}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{((universal-set1) or set3) and set2}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{(universal-(set1 or set3)) and (universal-set2)}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{(set1 or (universal-set2)) and set3}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "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>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(15..30)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "b+random(10..a-b)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(3..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(5..c-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "f": {"definition": "random(2,3,5,6)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "universal": {"definition": "set(1..a)", "templateType": "anything", "group": "Ungrouped variables", "name": "universal", "description": ""}, "set1": {"definition": "set(b..c)", "templateType": "anything", "group": "Ungrouped variables", "name": "set1", "description": ""}, "set2": {"definition": "set(d+1..a)", "templateType": "anything", "group": "Ungrouped variables", "name": "set2", "description": ""}, "set3": {"definition": "set(mod_set(1,a,f))", "templateType": "anything", "group": "Ungrouped variables", "name": "set3", "description": ""}}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Mark Hodds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/510/"}]}]}], "contributors": [{"name": "Mark Hodds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/510/"}]}