// Numbas version: exam_results_page_options {"name": "Union, complement, intersection", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Union, complement, intersection", "tags": ["complement", "elements", "intersection", "predicates", "set operations", "sets", "subsets", "union"], "metadata": {"description": "
Given some random finite subsets of the natural numbers, perform set operations $\\cap,\\;\\cup$ and complement.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "In this question, the universal set is $\\mathcal{U}=\\{x \\in \\mathbb{N}\\; | \\;x \\leq \\var{a}\\}$.
\nLet:
\n$A=\\{x \\in \\mathbb{N}\\;|\\;\\var{b}\\leq x \\leq \\var{c}\\}$.
\n$B=\\{x \\in \\mathbb{N}\\;|\\;x \\gt \\var{d}\\}$.
\n$C=\\{ x \\in \\mathbb{N}\\;|\\; x \\text{ divisible by } \\var{f}\\}$.
\n\n", "advice": "", "rulesets": {}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(15..30)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "b+random(10..a-b)-1", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(3..8)", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(5..c-1)", "description": "", "templateType": "anything"}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(2,3,5,6)", "description": "", "templateType": "anything"}, "universal": {"name": "universal", "group": "Ungrouped variables", "definition": "set(1..a)", "description": "", "templateType": "anything"}, "set1": {"name": "set1", "group": "Ungrouped variables", "definition": "set(b..c)", "description": "", "templateType": "anything"}, "set2": {"name": "set2", "group": "Ungrouped variables", "definition": "set(d+1..a)", "description": "", "templateType": "anything"}, "set3": {"name": "set3", "group": "Ungrouped variables", "definition": "set(mod_set(1,a,f))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "universal", "set1", "set2", "set3"], "variable_groups": [], "functions": {"mod_set": {"parameters": [["a", "number"], ["b", "number"], ["c", "number"]], "type": "list", "language": "javascript", "definition": "//returns all integers which are divisible by c betweeen a and b\nvar l=[];\nfor(var i=a;iEnumerate the following sets:\na) $A \\cap B=\\;$[[0]]
\nb) $B \\cap C=\\;$[[1]]
\nc) $A \\cap \\overline{C}=\\;$[[2]]
\nd) $(\\overline{A} \\cup C) \\cap B=\\;$[[3]]
\n\nNote that you input sets in the form set(a,b,c,..,z)
.
For example set(1,2,3)
gives the set $\\{1,2,3\\}$.
The empty set is input as set()
.
Also some labour saving tips:
\nIf you want to input all integers between $a$ and $b$ inclusive then instead of writing all the elements you can input this as set(a..b)
.
If you want to input all integers between $a$ and $b$ inclusive in steps of $c$ then this is input as set(a..b#c)
. So all odd integers from $-3$ to $28$ are input as set(-3..28#2).