// Numbas version: exam_results_page_options
{"name": "Basic Set Theory: power set", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "preamble": {"css": "", "js": ""}, "parts": [{"answer": "{PB}", "useCustomName": false, "customMarkingAlgorithm": "", "marks": 1, "variableReplacements": [], "vsetRangePoints": 5, "customName": "", "vsetRange": [0, 1], "prompt": "<p>What is the power set of $\\left\\{\\var{listB[0]},\\var{listB[1]}\\right\\}$?</p>", "variableReplacementStrategy": "originalfirst", "failureRate": 1, "checkingType": "absdiff", "steps": [{"answer": "set()", "useCustomName": false, "customMarkingAlgorithm": "", "marks": 1, "variableReplacements": [], "vsetRangePoints": 5, "customName": "", "vsetRange": [0, 1], "prompt": "<p>First we look at all the subsets containing zero elements. This is the empty set $\\left\\{\\right\\}$ and it is an element of any power set. Enter the empty set below using the NUMBAS syntax, which is <code>set()</code>.</p>", "variableReplacementStrategy": "originalfirst", "failureRate": 1, "checkingType": "absdiff", "adaptiveMarkingPenalty": 0, "valuegenerators": [], "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "unitTests": [], "showPreview": true, "type": "jme", "scripts": {}, "checkingAccuracy": 0.001, "showCorrectAnswer": true, "showFeedbackIcon": true}, {"answer": "set({listB[0]})", "useCustomName": false, "customMarkingAlgorithm": "", "marks": 1, "variableReplacements": [], "vsetRangePoints": 5, "customName": "", "vsetRange": [0, 1], "prompt": "<p>Next we look at all the subsets containing exactly one element, such as $\\left\\{\\var{listB[0]}\\right\\}$. Enter this using the NUMBAS syntax <code>set({listB[0]}).</code></p>", "variableReplacementStrategy": "originalfirst", "failureRate": 1, "checkingType": "absdiff", "adaptiveMarkingPenalty": 0, "valuegenerators": [], "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "unitTests": [], "showPreview": true, "type": "jme", "scripts": {}, "checkingAccuracy": 0.001, "showCorrectAnswer": true, "showFeedbackIcon": true}, {"answer": "set({listB[1]})", "useCustomName": false, "customMarkingAlgorithm": "", "marks": 1, "variableReplacements": [], "vsetRangePoints": 5, "customName": "", "vsetRange": [0, 1], "prompt": "<p>What is the other subset that that contains exactly one element?</p>", "variableReplacementStrategy": "originalfirst", "failureRate": 1, "checkingType": "absdiff", "adaptiveMarkingPenalty": 0, "valuegenerators": [], "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "unitTests": [], "showPreview": true, "type": "jme", "scripts": {}, "checkingAccuracy": 0.001, "showCorrectAnswer": true, "showFeedbackIcon": true}, {"answer": "{B}", "useCustomName": false, "customMarkingAlgorithm": "", "marks": 1, "variableReplacements": [], "vsetRangePoints": 5, "customName": "", "vsetRange": [0, 1], "prompt": "<p>What is the subset that contains exactly two elements?</p>", "variableReplacementStrategy": "originalfirst", "failureRate": 1, "checkingType": "absdiff", "adaptiveMarkingPenalty": 0, "valuegenerators": [], "extendBaseMarkingAlgorithm": true, "checkVariableNames": true, "unitTests": [], "showPreview": true, "type": "jme", "scripts": {}, "checkingAccuracy": 0.001, "showCorrectAnswer": true, "showFeedbackIcon": true}, {"prompt": "<p>The power set is the set containg all these answers as elements. Enter your answer using the NUMBAS syntax <code>set(a,b,c,d)</code> where $a,b,c$ and $d$ are your answers above.</p>", "useCustomName": false, "customMarkingAlgorithm": "", "marks": 0, "variableReplacements": [], "unitTests": [], "customName": "", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "information", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0}], "adaptiveMarkingPenalty": 0, "valuegenerators": [], "extendBaseMarkingAlgorithm": true, "checkVariableNames": true, "unitTests": [], "showPreview": true, "stepsPenalty": 0, "type": "jme", "scripts": {"mark": {"script": "\n\nvar variables = this.question.scope.variables;\nvar unwrap = Numbas.jme.unwrapValue;\nvar b1 = unwrap(variables.b1);\nvar b2 = unwrap(variables.b2);\n\nfunction setToStr(setofthings) {\n  var s = \"$\\\\left\\\\{\";\n  \n  for (var i = 0; i < setofthings.length; i++)\n  {\n    s += setofthings[i].value;\n    if (i < setofthings.length - 1)\n      s += \",\";\n  }\n  \n  return s + \"\\\\right\\\\}$\";\n}\n\nvar b_expression = \"set(set(),set(\" + b1 + \"), set(\" +b2 + \"), set(\"+b1+\",\"+b2+\"))\";\nvar tree;\ntry {\n  tree = Numbas.jme.compile(this.studentAnswer + \"- set()\");\n  var ans = unwrap(Numbas.jme.evaluate(tree,this.question.scope));\n  \n  // check answer has correct length\n  if (ans.length != 4)\n  {\n    this.setCredit(0,\"Your answer should be a set of $4$ elements\");\n    return;\n  }\n  \n   \n  // look for elements of the answer that are not in b\n  tree = Numbas.jme.compile(this.studentAnswer + \" - \" + b_expression);\n  var ans_b = unwrap(Numbas.jme.evaluate(tree,this.question.scope));\n  for (var i = 0; i < ans_b.length; i++)\n  {\n    if (\"set\" != ans_b[i].type)\n      this.setCredit(0, \"$\" + ans[i].value + \"$ is not a subset of $\\\\left\\\\{\" + b1 + \",\" + b2 + \"\\\\right\\\\}$.\");\n    \n    else\n      this.setCredit(0, setToStr(ans_b[i].value) + \" is not a subset of $\\\\left\\\\{\" + b1 + \",\" + b2 + \"\\\\right\\\\}$.\");\n  }\n  \n  tree = Numbas.jme.compile(b_expression + \" - \" + this.studentAnswer);\n  var b_ans = unwrap(Numbas.jme.evaluate(tree,this.question.scope));\n  for (var i = 0; i < ans_b.length; i++)\n  {\n    this.setCredit(0, setToStr(b_ans[i].value) + \" is a subset of $\\\\left\\\\{\" + b1 + \",\" + b2 + \"\\\\right\\\\}$ but it is not in your answer.\");\n  }\n  \n  if (0 == ans_b.length && 0 == b_ans.length) \n  {\n    this.setCredit(1, \"This is the power set.\");\n  }\n  \n}\ncatch(e) {\n    this.markingComment(e);\n}", "order": "instead"}}, "checkingAccuracy": 0.001, "showCorrectAnswer": true, "showFeedbackIcon": true}], "statement": "<p style=\"text-align: left;\">The <strong>power set</strong> of $A$, written $P(A)$, is the set of all subsets of $A$. </p>", "variables": {"listB": {"name": "listB", "description": "", "templateType": "anything", "definition": "[b1,b2]", "group": "Ungrouped variables"}, "b1": {"name": "b1", "description": "", "templateType": "anything", "definition": "random(0..9)", "group": "Ungrouped variables"}, "B": {"name": "B", "description": "", "templateType": "anything", "definition": "set(listB)", "group": "Ungrouped variables"}, "b2": {"name": "b2", "description": "", "templateType": "anything", "definition": "random(0..9 except b1)", "group": "Ungrouped variables"}, "PB": {"name": "PB", "description": "", "templateType": "anything", "definition": "set(set(),set(listB[0]),set(listB[1]),B)", "group": "Ungrouped variables"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "<p>Introductory exercise about power sets.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "ungrouped_variables": ["listB", "PB", "B", "b1", "b2"], "advice": "<p style=\"text-align: left;\">The power set of $\\left\\{\\var{listB[0]},\\var{listB[1]}\\right\\}$ is </p>\n<p style=\"text-align: center;\">$\\left\\{\\left\\{\\right\\}, \\left\\{\\var{listB[0]}\\right\\},\\left\\{\\var{listB[1]}\\right\\}, \\left\\{\\var{listB[0]},\\var{listB[1]}\\right\\}\\right\\}$.</p>\n<p style=\"text-align: left;\">You can obtain the power set by finding all the subsets of all possible sizes. Since we have a set of size two then the subsets have length at most two. These are</p>\n<ul>\n<li style=\"text-align: left;\">the subset of length zero: $\\left\\{\\right\\}$</li>\n<li style=\"text-align: left;\">the subsets of length one: $\\left\\{\\var{listB[0]}\\right\\},\\left\\{\\var{listB[1]}\\right\\}$</li>\n<li style=\"text-align: left;\">the subset length two: $\\left\\{\\var{listB[0]},\\var{listB[1]}\\right\\}$.</li>\n</ul>\n<p>Note that the length zero subset is always the empty set, and the largest subset is the set itself.</p>", "extensions": [], "functions": {}, "name": "Basic Set Theory: power set", "variable_groups": [], "tags": [], "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/"}]}]}], "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/"}]}