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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)HardLevel 10

If n(A) = 45, n(B) = 52 and n(A ∪ B) = 73, what is n(A △ B), where A △ B = (A − B) ∪ (B − A)?

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Answer and explanation

Correct answer: 49

First use the two-set union formula: n(A ∩ B) = n(A) + n(B) − n(A ∪ B) = 45 + 52 − 73 = 24. The symmetric difference contains the elements in exactly one set, so it excludes the common part. Hence n(A △ B) = n(A ∪ B) − n(A ∩ B) = 73 − 24 = 49. Option A is correct.

Tags

setssymmetric differenceunion and intersectionvenn diagramsOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

49

Why is this the correct answer?

First use the two-set union formula: n(A ∩ B) = n(A) + n(B) − n(A ∪ B) = 45 + 52 − 73 = 24. The symmetric difference contains the elements in exactly one set, so it excludes the common part. Hence n(A △ B) = n(A ∪ B) − n(A ∩ B) = 73 − 24 = 49. Option A is correct.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).

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