// Numbas version: exam_results_page_options
{"name": "Ensemble : unions, intersections et compl\u00e9mentaires", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "variable_groups": [], "name": "Ensemble : unions, intersections et compl\u00e9mentaires", "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"js": "", "css": ""}, "statement": "<p>Dans cette question, l'ensemble&nbsp; $ \\mathcal{E}$ est d&eacute;fini par $\\mathcal{E}=\\{n \\in \\mathbb{N}\\; | \\;n \\leq \\var{a}\\}$.</p>\n<p>Soit:</p>\n<p>$A=\\{n \\in \\mathbb{N}\\;|\\;\\var{b}\\leq x \\leq \\var{c}\\}$.</p>\n<p>$B=\\{n \\in \\mathbb{N}\\;|\\;n \\gt \\var{d}\\}$.</p>\n<p>$C=\\{ n \\in \\mathbb{N}\\;|\\; n \\text{ divisible par } \\var{f}\\}$.</p>\n<p></p>\n<p></p>", "extensions": [], "ungrouped_variables": ["a", "b", "c", "d", "f", "universal", "set1", "set2", "set3"], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>On a plusieurs ensembles dont les &eacute;l&eacute;ments sont des entiers tir&eacute;s al&eacute;atoirement. Il faut faire des op&eacute;rations &eacute;l&eacute;mentaires faisant intervenir&nbsp; $\\cap,\\;\\cup$ et la notion de compl&eacute;mentaire.</p>"}, "parts": [{"unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "<p>Donnez les ensembles suivants:</p>\n<p>Vous &eacute;crirez les ensembles sous la forme <code>set(a,b,c,..,z). L'ensemble vide est not&eacute; </code><code>set()</code>.</p>\n<p>a) $A \\cup C=\\;$[[0]]</p>\n<p>b) $\\overline{B} \\cap C=\\;$[[1]]</p>\n<p>c) $A \\cup \\overline{B}=\\;$[[2]]</p>\n<p>d) $(A \\cap B) \\cup C=\\;$[[3]]</p>\n<p></p>\n<p></p>\n<p></p>", "type": "gapfill", "gaps": [{"unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "checkingType": "absdiff", "scripts": {}, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "type": "jme", "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "expectedVariableNames": [], "failureRate": 1, "vsetRange": [0, 1], "vsetRangePoints": 5, "showCorrectAnswer": true, "showPreview": true, "answer": "{set1 or set3}", "variableReplacementStrategy": "originalfirst", "marks": 1}, {"unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "checkingType": "absdiff", "scripts": {}, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "type": "jme", "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "expectedVariableNames": [], "failureRate": 1, "vsetRange": [0, 1], "vsetRangePoints": 5, "showCorrectAnswer": true, "showPreview": true, "answer": "{(universal - set2) and set3}", "variableReplacementStrategy": "originalfirst", "marks": "2"}, {"unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "checkingType": "absdiff", "scripts": {}, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "type": "jme", "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "expectedVariableNames": [], "failureRate": 1, "vsetRange": [0, 1], "vsetRangePoints": 5, "showCorrectAnswer": true, "showPreview": true, "answer": "{set1 or (universal-set2)}", "variableReplacementStrategy": "originalfirst", "marks": "2"}, {"unitTests": [], "variableReplacements": [], "showFeedbackIcon": true, "checkingType": "absdiff", "scripts": {}, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "type": "jme", "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "expectedVariableNames": [], "failureRate": 1, "vsetRange": [0, 1], "vsetRangePoints": 5, "showCorrectAnswer": true, "showPreview": true, "answer": "{(set1 and set2) or set3}", "variableReplacementStrategy": "originalfirst", "marks": "1"}], "customMarkingAlgorithm": "", "sortAnswers": false, "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 0}], "variables": {"set3": {"group": "Ungrouped variables", "name": "set3", "definition": "set(mod_set(f,a,f))", "description": "", "templateType": "anything"}, "universal": {"group": "Ungrouped variables", "name": "universal", "definition": "set(1..a)", "description": "", "templateType": "anything"}, "set2": {"group": "Ungrouped variables", "name": "set2", "definition": "set(d+1..a)", "description": "", "templateType": "anything"}, "f": {"group": "Ungrouped variables", "name": "f", "definition": "random(2,3,5,6)", "description": "", "templateType": "anything"}, "a": {"group": "Ungrouped variables", "name": "a", "definition": "random(12..24)", "description": "", "templateType": "anything"}, "c": {"group": "Ungrouped variables", "name": "c", "definition": "b+random(10..a-b)", "description": "", "templateType": "anything"}, "b": {"group": "Ungrouped variables", "name": "b", "definition": "random(3..8)", "description": "", "templateType": "anything"}, "set1": {"group": "Ungrouped variables", "name": "set1", "definition": "set(b..c)", "description": "", "templateType": "anything"}, "d": {"group": "Ungrouped variables", "name": "d", "definition": "random(5..c-1)", "description": "", "templateType": "anything"}}, "rulesets": {}, "functions": {"mod_set": {"parameters": [["a", "number"], ["b", "number"], ["c", "number"]], "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", "language": "javascript", "type": "list"}}, "advice": "", "type": "question", "contributors": [{"name": "Hollie Tarr", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1176/"}, {"name": "Jeanne Parmentier", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2126/"}]}]}], "contributors": [{"name": "Hollie Tarr", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1176/"}, {"name": "Jeanne Parmentier", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2126/"}]}