// Numbas version: exam_results_page_options
{"name": "Mengenlehre: Teilmengen und Mengengleichheit", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Mengenlehre: Teilmengen und Mengengleichheit", "tags": [], "metadata": {"description": "<p>Introductory exercise about set equality</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>Nehmen wir an, wir haben die drei Elemente $1, 1$ und $2$. Wenn wir diese als ungeordnete Zusammenstellung einzelner unterscheidbarer Objekte auffassen dann nennen wir dies die <strong>Menge</strong>&nbsp;$\\left\\{1,1,2\\right\\}$. Weil Mengen ungeordnet sind, ist das dieselbe Menge wie $\\left\\{2,1,1\\right\\}$ und&nbsp;weil wir nur unterscheidbare Objekte zusammenstellen auch dieselbe Menge wie $\\left\\{1,2\\right\\}$.</p>\n<p>Nehmen wir als Beispiel die folgenden Mengen her:&nbsp;$A=\\left\\{\\var{A[0]},\\var{A[1]},\\var{A[2]},\\var{A[3]}\\right\\}, B=\\left\\{\\var{B[0]},\\var{B[1]},\\var{B[2]},\\var{B[3]},\\var{B[4]}\\right\\}$ und $C=\\left\\{\\var{C[0]},\\var{C[1]},\\var{C[2]},\\var{C[3]},\\var{C[4]},\\var{C[5]}\\right\\}$.</p>", "advice": "<p>Sie k&ouml;nnen &uuml;berpr&uuml;fen, ob&nbsp;$M \\subset N$ ist, in dem Sie nach und nach f&uuml;r jedes Element von&nbsp;$M$ pr&uuml;fen, ob es auch in $N$ enthalten ist. Es sind 6 Aussagen zu pr&uuml;fen, also m&uuml;ssen Sie das Ganze sechs mal so machen.</p>\n<hr/>\n<p>Der zweite Teil baut auf dem ersten auf. Sie m&uuml;ssen sich Ihre Antworten ansehen und nachschauen, welche Mengen einander als Teilmengen enthalten.&nbsp;Das ist sehr &auml;hnlich wie bei der&nbsp;'kleiner oder gleich'-Relation&nbsp;insofern Sie, wenn Sie zwei Zahlen $x$ und $y$ haben bei denen&nbsp;$x \\leq y$ und $y\\leq x$ gilt,&nbsp;dann eben auch $x=y$ gelten muss.</p>", "rulesets": {}, "extensions": [], "variables": {"B": {"name": "B", "group": "Ungrouped variables", "definition": "repeat(random(1..4),5)", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "repeat(random(1..4),4)", "description": "", "templateType": "anything"}, "BsubsetC": {"name": "BsubsetC", "group": "Ungrouped variables", "definition": "if(set(B)=intersection(set(C),set(B)),1,0)", "description": "", "templateType": "anything"}, "BsubsetA": {"name": "BsubsetA", "group": "Ungrouped variables", "definition": "if(set(B)=intersection(set(A),set(B)),1,0)", "description": "", "templateType": "anything"}, "AB": {"name": "AB", "group": "Ungrouped variables", "definition": "if(set(A) = set(B),1,0)", "description": "", "templateType": "anything"}, "AsubsetB": {"name": "AsubsetB", "group": "Ungrouped variables", "definition": "if(set(A)=intersection(set(A),set(B)),1,0)", "description": "", "templateType": "anything"}, "BC": {"name": "BC", "group": "Ungrouped variables", "definition": "if(set(B) = set(C),1,0)", "description": "", "templateType": "anything"}, "CsubsetB": {"name": "CsubsetB", "group": "Ungrouped variables", "definition": "if(set(C)=intersection(set(C),set(B)),1,0)", "description": "", "templateType": "anything"}, "CA": {"name": "CA", "group": "Ungrouped variables", "definition": "if(set(C) = set(A),1,0)", "description": "", "templateType": "anything"}, "CsubsetA": {"name": "CsubsetA", "group": "Ungrouped variables", "definition": "if(set(C)=intersection(set(A),set(C)),1,0)", "description": "", "templateType": "anything"}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "repeat(random(1..4),6)", "description": "", "templateType": "anything"}, "AsubsetC": {"name": "AsubsetC", "group": "Ungrouped variables", "definition": "if(set(A)=intersection(set(A),set(C)),1,0)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "AB + BC + CA =1 and AsubsetB + BsubsetA + AsubsetC + CsubsetA + BsubsetC + CsubsetB=4", "maxRuns": 100}, "ungrouped_variables": ["A", "B", "C", "AB", "BC", "CA", "AsubsetB", "BsubsetA", "CsubsetB", "BsubsetC", "CsubsetA", "AsubsetC"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "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>Wenn jedes Elememt der Menge $M$&nbsp;auch ein Element der Menge $N$&nbsp;ist, dann nennen wir&nbsp;$M$&nbsp;eine&nbsp;<strong>Teilmenge</strong>&nbsp;von $N$: $M \\subseteq N$. Welche der oben angegebenen Mengen sind Teilmengen voneinander?</p>\n<p><em>Kreuzen Sie alle korrekten Antworten an!</em></p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["<p>$A \\subseteq B$</p>", "<p>$B \\subseteq A$</p>", "<p>$C \\subseteq B$</p>", "<p>$B \\subseteq C$</p>", "<p>$C \\subseteq A$</p>", "<p>$A \\subseteq C$</p>"], "matrix": ["AsubsetB", "BsubsetA", "CsubsetB", "BsubsetC", "CsubsetA", "AsubsetC"], "distractors": ["", "", "", "", "", ""]}, {"type": "m_n_2", "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>Mengen sind gleich, wenn Sie gegenseitige Teilmengen voneinander sind. Welche der Mengen sind gleich?</p>\n<p><em>Kreuzen Sie&nbsp;die korrekte Antwort an!</em></p>\n<p><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 74px; width: 0px; top: 76px; height: 0px;\"></span><span style=\"z-index: 2147483647; position: absolute; visibility: hidden; left: 59px; width: 50px; top: 61px; height: 20px; font-size: 10px; color: black;\"></span></p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["<p>$A=B$</p>", "<p>$B=C$</p>", "<p>$C=A$</p>"], "matrix": ["AB", "BC", "CA"], "distractors": ["", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Daniel Mansfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/743/"}, {"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}]}], "contributors": [{"name": "Daniel Mansfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/743/"}, {"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}