// Numbas version: exam_results_page_options
{"name": "Weitere \u00dcbungen (Lektion 2)", "metadata": {"description": "<p>&Uuml;bungen zu Mengenlehre und Beweisprinzipien</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["Teilmengen und Mengengleichheit", "", "", ""], "questions": [{"name": "Mengenlehre: Teilmengen und Mengengleichheit", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "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/"}], "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": {}, "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"}, {"name": "Operationen mit Mengen", "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}, "contributors": [{"name": "Daniel Mansfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/743/"}, {"name": "Sean Gardiner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2443/"}, {"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "<p>Simple exercises introducing the fundamental set operations, and NUMBAS syntax for sets.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>Betrachten Sie die Mengen&nbsp;$A = \\var{A}$ und $B = \\var{B}$. Bestimmen Sie die Vereinigungsmenge, die Schnittmenge und die Differenzmengen.&nbsp;</p>\n<p><em>Benutzen Sie dabei bitte die Schreibweise z.B.</em>&nbsp;<code>set(1,2,3)</code> <em>f&uuml;r die Menge</em> $\\left\\{1,2,3\\right\\}$.</p>", "advice": "<p>Die Vereinigungsmenge ist die Menge aller Elemente aus&nbsp;einer der beiden Mengen.</p>\n<p style=\"text-align: center;\">$ A \\cup B = \\left\\{ x\\, |\\, x \\in A \\text{ or } x \\in B\\right\\}$</p>\n<hr/>\n<p style=\"text-align: left;\">Die Schnittmenge ist die Menge aller Elemente, die in beiden Mangen enthalten sind.</p>\n<p style=\"text-align: center;\">$ A \\cap B = \\left\\{ x\\, |\\, x \\in A \\text{ and } x \\in B\\right\\}$</p>\n<hr/>\n<p style=\"text-align: left;\">Die Differenzmenge&nbsp;$A\\setminus B$ ist die Menge der Elemente aus $A$, welche nicht in$B$ enthalten sind:</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;\">Analog, ist $B\\setminus A$ is die Menge der Elemente aus $B$, die nicht in $A$ enthalten sind:</p>\n<p style=\"text-align: center;\">$ B - A = \\left\\{ x \\in B |\\, x \\notin A\\right\\}$</p>\n<hr/>\n<p style=\"text-align: left;\">Die symmetrische Differenz&nbsp;$A \\Delta B$ is die Vereinigung der beiden Differenzmengen,&nbsp;kann aber auch als Vereinigungsmenge minus Schnittmenge dargestellt werden:</p>\n<p style=\"text-align: center;\">$ A \\Delta B = (A \\cup B) - (A \\cap B)$.</p>", "rulesets": {}, "variables": {"listA": {"name": "listA", "group": "Ungrouped variables", "definition": "repeat(random(5..9),4)", "description": "", "templateType": "anything"}, "listN": {"name": "listN", "group": "Ungrouped variables", "definition": "repeat(random(1..9),2)", "description": "", "templateType": "anything"}, "listB": {"name": "listB", "group": "Ungrouped variables", "definition": "repeat(random(0..4),4)", "description": "", "templateType": "anything"}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "union(set(listB),set(listN))", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "union(set(listA),set(listN))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "not(listA = listB)", "maxRuns": 100}, "ungrouped_variables": ["listA", "listB", "A", "B", "listN"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"validate": {"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}", "order": "instead"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Was ist die Vereinigungsmenge&nbsp;$A \\cup B$?</p>", "answer": "{union(A,B)}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"validate": {"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}", "order": "instead"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Was ist die Schnittmenge&nbsp;$A \\cap B$?</p>", "answer": "{intersection(A,B)}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"validate": {"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}", "order": "instead"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Was ist $A\\setminus B$,&nbsp;die&nbsp;Menge der Elemente von $A$&nbsp;die nicht in $B$ enthalten ist?</p>", "answer": "{A-B}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"validate": {"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}", "order": "instead"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Was ist $B\\setminus A$,&nbsp;die&nbsp;Menge der Elemente von $B$ die nicht in $A$ enthalten ist?</p>", "answer": "{B-A}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"validate": {"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}", "order": "instead"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What ist die Vereinigung der Differenzmengen $(A\\setminus B)\\cup(B\\setminus A)$?&nbsp;Diese Menge hei&szlig;t auch&nbsp;<strong>symmetrische Differenz</strong>&nbsp;$A\\Delta B$.</p>", "answer": "{union(A-B,B-A)}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "m_n_x", "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>Ordnen Sie zu: Welche Menge geh&ouml;rt zu welchem&nbsp;Venn-Diagramm, wenn der linke Kreis&nbsp;die Menge&nbsp;$A$ und&nbsp;der rechte Kreis die Menge $B$ darstellt.</p>\n<p></p>", "minMarks": 0, "maxMarks": "1", "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "choices": ["<p>$A\\cup B$</p>", "<p>$A \\cap B$</p>", "<p>$A \\Delta B$</p>", "<p>$A \\setminus B$</p>"], "matrix": [["0.25", 0, 0, 0], [0, "0.25", 0, 0], [0, 0, "0.25", 0], [0, 0, 0, "0.25"]], "layout": {"type": "all", "expression": ""}, "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>"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Wahrheitstabelle", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "<p>Einfache Wahrheitstabelle mit zwei Aussagen</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "<p>F&uuml;r die Aussagen $A$ und $B$ sei die folgende kombinierte Aussage gegeben:&nbsp;{full_tex}.</p>\n<p>Vervollst&auml;ndigen Sie die zugeh&ouml;rige Wahrheitstabelle!</p>", "advice": "<p>Sie k&ouml;nnen oben die korrekten&nbsp;Eintragungen sehen.</p>\n<p></p>", "rulesets": {}, "variables": {"w": {"name": "w", "group": "Ungrouped variables", "definition": "true", "description": "", "templateType": "anything"}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything"}, "combinations": {"name": "combinations", "group": "Ungrouped variables", "definition": "['&&','||',' implies ']", "description": "", "templateType": "anything"}, "combinations_tex": {"name": "combinations_tex", "group": "Ungrouped variables", "definition": "['\\\\wedge','\\\\vee','\\\\Rightarrow']\n", "description": "", "templateType": "anything"}, "index1": {"name": "index1", "group": "Ungrouped variables", "definition": "shuffle_me[1]", "description": "", "templateType": "anything"}, "index2": {"name": "index2", "group": "Ungrouped variables", "definition": "shuffle_me[2]", "description": "", "templateType": "anything"}, "index3": {"name": "index3", "group": "Ungrouped variables", "definition": "shuffle_me[0]", "description": "", "templateType": "anything"}, "full_tex": {"name": "full_tex", "group": "Ungrouped variables", "definition": "'$\\\\left(A'+combinations_tex[index1]+' B\\\\right)'+combinations_tex[index2]+'\\\\left(A'+combinations_tex[index3]+' B\\\\right)$'", "description": "", "templateType": "anything"}, "full_ww": {"name": "full_ww", "group": "Ungrouped variables", "definition": "eval(expression('('+w+combinations[index1]+w+')'+combinations[index2]+'('+w+combinations[index3]+w+')'))", "description": "", "templateType": "anything"}, "full_wf": {"name": "full_wf", "group": "Ungrouped variables", "definition": "eval(expression('('+w+combinations[index1]+f+')'+combinations[index2]+'('+w+combinations[index3]+f+')'))", "description": "", "templateType": "anything"}, "full_fw": {"name": "full_fw", "group": "Ungrouped variables", "definition": "eval(expression('('+f+combinations[index1]+w+')'+combinations[index2]+'('+f+combinations[index3]+w+')'))", "description": "", "templateType": "anything"}, "full_ff": {"name": "full_ff", "group": "Ungrouped variables", "definition": "eval(expression('('+f+combinations[index1]+f+')'+combinations[index2]+'('+f+combinations[index3]+f+')'))", "description": "", "templateType": "anything"}, "one_list": {"name": "one_list", "group": "Ungrouped variables", "definition": "[eval(expression(w+combinations[index1]+w)),eval(expression(w+combinations[index1]+f)),eval(expression(f+combinations[index1]+w)),eval(expression(f+combinations[index1]+f))]", "description": "", "templateType": "anything"}, "three_list": {"name": "three_list", "group": "Ungrouped variables", "definition": "[eval(expression(w+combinations[index3]+w)),eval(expression(w+combinations[index3]+f)),eval(expression(f+combinations[index3]+w)),eval(expression(f+combinations[index3]+f))]", "description": "", "templateType": "anything"}, "column3": {"name": "column3", "group": "Ungrouped variables", "definition": "'$A'+combinations_tex[index3]+' B$'", "description": "", "templateType": "anything"}, "column1": {"name": "column1", "group": "Ungrouped variables", "definition": "'$A'+combinations_tex[index1]+' B$'", "description": "", "templateType": "anything"}, "shuffle_me": {"name": "shuffle_me", "group": "Ungrouped variables", "definition": "shuffle(0..2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["w", "f", "combinations", "combinations_tex", "index1", "index2", "index3", "full_tex", "full_ww", "full_wf", "full_fw", "full_ff", "one_list", "three_list", "column3", "column1", "shuffle_me"], "variable_groups": [], "functions": {"get_letter": {"parameters": [["a", "boolean"]], "type": "anything", "language": "jme", "definition": "if(a,'w','f')"}}, "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": "<table border=\"1\" cellspacing=\"3\" cellpadding=\"5\"><caption></caption>\n<tbody>\n<tr>\n<td>$A$</td>\n<td>$B$</td>\n<td>{column1}</td>\n<td>{column3}</td>\n<td>{full_tex}</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">w</td>\n<td style=\"text-align: center;\">w</td>\n<td style=\"text-align: center;\">[[0]]</td>\n<td style=\"text-align: center;\">[[4]]</td>\n<td style=\"text-align: center;\">[[8]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">w</td>\n<td style=\"text-align: center;\">f</td>\n<td style=\"text-align: center;\">[[1]]</td>\n<td style=\"text-align: center;\">[[5]]</td>\n<td style=\"text-align: center;\">[[9]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">f</td>\n<td style=\"text-align: center;\">w</td>\n<td style=\"text-align: center;\">[[2]]</td>\n<td style=\"text-align: center;\">[[6]]</td>\n<td style=\"text-align: center;\">[[10]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">f</td>\n<td style=\"text-align: center;\">f</td>\n<td style=\"text-align: center;\">[[3]]</td>\n<td style=\"text-align: center;\">[[7]]</td>\n<td style=\"text-align: center;\">[[11]]</td>\n</tr>\n</tbody>\n</table>", "gaps": [{"type": "patternmatch", "useCustomName": true, "customName": "one_ww", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{get_letter(one_list[0])}", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "one_wf", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{get_letter(one_list[1])}", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "one_fw", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{get_letter(one_list[2])}", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "one_ff", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{get_letter(one_list[3])}", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "three_ww", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{get_letter(three_list[0])}", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "three_wf", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{get_letter(three_list[1])}", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "three_fw", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{get_letter(three_list[2])}", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "three_ff", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{get_letter(three_list[3])}", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "full_ww", "marks": "0.7", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{get_letter(full_ww)}", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "full_wf", "marks": "0.7", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{get_letter(full_wf)}", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "full_fw", "marks": "0.7", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{get_letter(full_fw)}", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "full_ff", "marks": "0.7", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{get_letter(full_ff)}", "displayAnswer": "", "matchMode": "exact"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Vollst\u00e4ndige Induktion", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "<p>Ein einfacher, gef&uuml;hrter Induktionsbeweis</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "<p><strong>Zu zeigen:</strong> F&uuml;r alle $n\\in\\mathbb{N}$ gilt: $\\,\\var{a}^{n+1} + \\var{a + 1}^{2n&minus;1}$ ist durch $\\var{a^2 + a + 1}$ teilbar.</p>\n<p><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 870px; width: 0px; top: 31px; height: 0px;\"></span><span style=\"z-index: 2147483647; position: absolute; visibility: hidden; left: 855px; width: 50px; top: 16px; height: 20px; font-size: 10px; color: black;\"></span></p>", "advice": "<p>Induktionsanfang: Wir setzen 1 f&uuml;r $n$ ein:&nbsp;$A(1):\\ \\,\\var{a}^{1+1} + \\var{a + 1}^{2\\cdot 1&minus;1}=\\var{a}^{2} + \\var{a + 1}=\\var{a1}$, was offensichtlich durch $\\var{a1}$ teilbar ist.</p>\n<hr/>\n<p>Induktionsbehauptung: Wir setzen zun&auml;chst $(n+1)$ f&uuml;r $n$ ein:&nbsp;$A(n+1):\\ \\,\\var{a}^{(n+1)+1} + \\var{a + 1}^{2\\cdot(n+1)&minus;1}=\\var{a}^{n+2} + \\var{a + 1}^{2n+1}$</p>\n<p>Die Umformungsschritte nutzen dann die Potenzrechenregel&nbsp;$a^{(b+c)}=a^b+a^c$ und&nbsp;das Distibutivgesetz $(a+b)\\cdot c=a\\cdot c+b\\cdot c$&nbsp;</p>\n<p>Womit sich ergibt:</p>\n<p style=\"text-align: center;\">$A(n+1):\\ \\,\\var{a}^{n+2} +\\var{a + 1}^{2n+1}=\\var{k1}\\cdot\\,\\var{a}^{n+1} +\\var{k2}\\cdot\\,\\var{a + 1}^{2n&minus;1}$</p>\n<p style=\"text-align: center;\"><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 559px; width: 0px; top: 99px; height: 0px;\"></span>$=\\var{k1}\\cdot\\,\\var{a}^{n+1} +\\var{k1}\\cdot\\,\\var{a + 1}^{2n&minus;1}+\\var{k2-k1}\\cdot\\,\\var{a + 1}^{2n&minus;1}=\\var{k3}\\cdot\\left(\\var{a}^{n+1} + \\var{a + 1}^{2n&minus;1}\\right)+\\var{k4}\\cdot\\,\\var{a + 1}^{2n&minus;1}$</p>\n<p>Der erste Summand ist gem&auml;&szlig; Induktionsvoraussetzung durch $\\var{a1}$ teilbar, der zweite Summand, weil er ein Vielfaches von $\\var{a1}$ ist. Die Summe ist dann auch durch $\\var{a1}$ teilbar.</p>", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything"}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "a^2+a+1", "description": "", "templateType": "anything"}, "k2": {"name": "k2", "group": "Ungrouped variables", "definition": "(a+1)^2", "description": "", "templateType": "anything"}, "k1": {"name": "k1", "group": "Ungrouped variables", "definition": "a", "description": "", "templateType": "anything"}, "k3": {"name": "k3", "group": "Ungrouped variables", "definition": "a", "description": "", "templateType": "anything"}, "k4": {"name": "k4", "group": "Ungrouped variables", "definition": "a^2+a+1", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "a1", "k2", "k1", "k3", "k4"], "variable_groups": [], "functions": {}, "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><strong>Induktionsanfang $A(1)$:</strong></p>\n<p>Durch Einsetzen ergibt sich:&nbsp;[[0]], was ein ganzzahliges Vielfaches von $\\var{a^2 + a + 1}$ ist.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "IA", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "a1", "maxValue": "a1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}, {"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><strong>Induktionsschluss $A(n)\\Rightarrow A(n+1)$:</strong></p>\n<p>Es ist zu zeigen, dass unter der <strong>Induktionsvoraussetzung</strong></p>\n<p style=\"text-align: center;\">$A(n):\\ \\,\\var{a}^{n+1} + \\var{a + 1}^{2n&minus;1}$ ist durch $\\var{a^2 + a + 1}$ teilbar (f&uuml;r beliebiges aber festes $n$)</p>\n<p>die <strong>Induktionsbehauptung</strong></p>\n<p style=\"text-align: center;\">$A(n+1):\\,$ [[0]] ist durch $\\var{a^2 + a + 1}$ teilbar&nbsp;</p>\n<p>richtig ist.</p>\n<p>Wir&nbsp;formen jetzt den Term in der Aussage $A(n+1)$ so um, dass wir den Term aus der Aussage $A(n)$ wieder erkennen, dazu heben wir wie folgt heraus:</p>\n<p style=\"text-align: center;\">$A(n+1):\\,$&nbsp;[[0]]$=$[[1]]$\\cdot\\,\\var{a}^{n+1} +$[[2]]$\\cdot\\,\\var{a + 1}^{2n&minus;1}$</p>\n<p><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 559px; width: 0px; top: 99px; height: 0px;\"></span><span style=\"z-index: 2147483647; position: absolute; visibility: hidden; left: 544px; width: 50px; top: 84px; height: 20px; font-size: 10px; color: black;\"></span>als n&auml;chstes m&uuml;ssen wir den gesamten Term $\\var{a}^{n+1} + \\var{a + 1}^{2n&minus;1}$ herausheben:</p>\n<p style=\"text-align: center;\">$\\qquad\\qquad=$[[3]]$\\cdot\\left(\\var{a}^{n+1} + \\var{a + 1}^{2n&minus;1}\\right)+$[[4]]$\\cdot\\,\\var{a + 1}^{2n&minus;1}$</p>\n<p style=\"text-align: left;\">Dieser Term ist durch&nbsp;$\\var{a^2 + a + 1}$ teilbar, weil es der erste&nbsp;Summand wegen der Induktionsvoraussetzung ist, warum es auch der zweite ist, erkennen Sie, wenn Sie korrekt herausgehoben haben. Sind zwei Summanden durch eine Zahl teilbar, dann ist es immer auch deren Summe.</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "IB", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a}^(n+2) + {a + 1}^(2n+1)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "n", "value": ""}]}, {"type": "numberentry", "useCustomName": true, "customName": "k1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "k1", "maxValue": "k1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "eu"}, {"type": "numberentry", "useCustomName": true, "customName": "k2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "k2", "maxValue": "k2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "eu"}, {"type": "numberentry", "useCustomName": true, "customName": "k3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "k3", "maxValue": "k3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "eu"}, {"type": "numberentry", "useCustomName": true, "customName": "k4", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "k4", "maxValue": "k4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "eu"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "menu", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "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"]]}