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Simple exercises introducing the fundamental set operations, and NUMBAS syntax for sets.
", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "", "advice": "The union of two sets is the set of elements from either set
\n$ A \\cup B = \\left\\{ x\\, |\\, x \\in A \\text{ or } x \\in B\\right\\}$
\nThe intersetction of two sets is the set of elements common to both sets
\n$ A \\cap B = \\left\\{ x\\, |\\, x \\in A \\text{ and } x \\in B\\right\\}$
\nThe difference $A-B$ is the set of elements from $A$ which are not in $B$:
\n$ A - B = \\left\\{ x \\in A |\\, x \\notin B\\right\\}$
\nSimilarly, the difference $B-A$ is the set of elements from $B$ which are not in $A$:
\n$ B - A = \\left\\{ x \\in B |\\, x \\notin A\\right\\}$
\nThe symmetric difference $A \\Delta B$ is the union of the set differences, but it can also be expressed as the union minus the intersection
\n$ A \\Delta B = (A \\cup B) - (A \\cap B)$.
", "rulesets": {}, "extensions": [], "variables": {"B": {"name": "B", "group": "Ungrouped variables", "definition": "union(set(listB),set(listN))", "description": "", "templateType": "anything"}, "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"}, "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": "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": "Welke notatie komt overeen met het rode deel op het venndiagram.
$A$ is de linkerverzameling en$B$ de rechterverzameling.
$A\\cup B$
", "$A \\cap B$
", "$A\\setminus B$
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\nZoek de unie, de doorsnede en het verschil.
\nGebruik de code set(1,2,3)
om $\\left\\{1,2,3\\right\\}$ te antwoorden.
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\n$A \\cap B$ = [[1]]
\n$A\\setminus B$ =[[2]]
\n$B\\setminus A$ =[[3]]
\n