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

If n(A) = 10, n(B) = 8, n(C) = 6, n(A ∩ B) = 3, n(A ∩ C) = 2, n(B ∩ C) = 1, and n(A ∩ B ∩ C) = 0, what is n(A ∪ B ∪ C)?

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Answer and explanation

Correct answer: 18

Use the inclusion–exclusion formula for three finite sets: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(A ∩ C) − n(B ∩ C) + n(A ∩ B ∩ C). Substitution gives 10 + 8 + 6 − 3 − 2 − 1 + 0 = 18. Thus, the union contains 18 elements. Pairwise overlaps are subtracted to avoid counting common elements twice.

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setsunioninclusion-exclusionvenn diagramsOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

18

Why is this the correct answer?

Use the inclusion–exclusion formula for three finite sets: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(A ∩ C) − n(B ∩ C) + n(A ∩ B ∩ C). Substitution gives 10 + 8 + 6 − 3 − 2 − 1 + 0 = 18. Thus, the union contains 18 elements. Pairwise overlaps are subtracted to avoid counting common elements twice.

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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