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

If n(A) = 8, n(B) = 6, and n(A ∪ B) = 10, what is n(A ∩ B)?

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Answer and explanation

Correct answer: 4

For two finite sets, the inclusion–exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Therefore, n(A ∩ B) = 8 + 6 − 10 = 4. Hence, four elements are common to A and B. Option 2 is merely the difference between the set sizes, 14 ignores the overlap, and 10 is the cardinality of the union.

Tags

setscardinalityintersectionunionOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

4

Why is this the correct answer?

For two finite sets, the inclusion–exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Therefore, n(A ∩ B) = 8 + 6 − 10 = 4. Hence, four elements are common to A and B. Option 2 is merely the difference between the set sizes, 14 ignores the overlap, and 10 is the cardinality of the union.

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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