// Numbas version: exam_results_page_options
{"name": "Power set - list members", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Power set - list members", "tags": [], "metadata": {"description": "<p>Introductory exercise about power sets.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "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>", "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>", "rulesets": {}, "extensions": [], "variables": {"PB": {"name": "PB", "group": "Ungrouped variables", "definition": "set(set(),set(listB[0]),set(listB[1]),B)", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "deal(2)", "description": "", "templateType": "anything"}, "listB": {"name": "listB", "group": "Ungrouped variables", "definition": "repeat(random(3..9),2)", "description": "", "templateType": "anything"}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "set(listB)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "not (listB[0] = listB[1])", "maxRuns": 100}, "ungrouped_variables": ["A", "listB", "PB", "B"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [{"variable": "B", "must_go_first": true}], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>What is the power set of $\\left\\{\\var{listB[0]},\\var{listB[1]}\\right\\}$?</p>\n<p>You can enter a set using the notation set(a,b,c). A set containing the set $\\{a\\}$ would be entered as set(set(a)).&nbsp;</p>", "answer": "{PB}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "valuegenerators": []}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}