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

If n(U) = 60, n(A) = 25, n(B) = 30, and 5 students are in neither set, what is n(A ∩ B)?

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Answer and explanation

Correct answer: 0

Five students are in neither A nor B, so the union contains 60 − 5 = 55 students. Apply the inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Thus 55 = 25 + 30 − n(A ∩ B), giving n(A ∩ B) = 0. Therefore, the two sets are disjoint in this situation.

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setsunionintersectioninclusion-exclusionOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

0

Why is this the correct answer?

Five students are in neither A nor B, so the union contains 60 − 5 = 55 students. Apply the inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Thus 55 = 25 + 30 − n(A ∩ B), giving n(A ∩ B) = 0. Therefore, the two sets are disjoint in this situation.

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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