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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)HardLevel 15

If n(A ∪ B ∪ C) = 100, n(A) = 50, n(B) = 45, n(C) = 40, n(A ∩ B) = 18, n(B ∩ C) = 15, and n(C ∩ A) = 12, what is n(A ∩ B ∩ C)?

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Answer and explanation

Correct answer: 10

Let x = n(A ∩ B ∩ C). The three-set inclusion-exclusion formula gives 100 = 50 + 45 + 40 − 18 − 15 − 12 + x. The known terms simplify to 90, so 100 = 90 + x and x = 10. The triple intersection must be added back because pairwise intersections overlap there, making option A correct.

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setsVenn diagramstriple intersectioninclusion-exclusionOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

10

Why is this the correct answer?

Let x = n(A ∩ B ∩ C). The three-set inclusion-exclusion formula gives 100 = 50 + 45 + 40 − 18 − 15 − 12 + x. The known terms simplify to 90, so 100 = 90 + x and x = 10. The triple intersection must be added back because pairwise intersections overlap there, making option A 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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