// Numbas version: finer_feedback_settings
{"name": "Operationen mit Mengen", "extensions": [], "custom_part_types": [], "resources": [["question-resources/384px-Venn0111.svg.png", "384px-Venn0111.svg.png"], ["question-resources/384px-Venn0001.svg.png", "384px-Venn0001.svg.png"], ["question-resources/384px-Venn0110.svg.png", "384px-Venn0110.svg.png"], ["question-resources/240px-Venn0100.svg.png", "240px-Venn0100.svg.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Operationen mit Mengen", "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": {}, "extensions": [], "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", "type": "question", "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/"}], "resources": ["question-resources/384px-Venn0111.svg.png", "question-resources/384px-Venn0001.svg.png", "question-resources/384px-Venn0110.svg.png", "question-resources/240px-Venn0100.svg.png"]}]}], "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/"}]}