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

If n(A − B) = 12, n(B − A) = 9, and n(A ∩ B) = 7, what is n(A ∪ B)?

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Answer and explanation

Correct answer: 28

The union is divided into three disjoint regions: elements only in A, counted by n(A − B) = 12; elements only in B, counted by n(B − A) = 9; and common elements, counted by n(A ∩ B) = 7. Therefore n(A ∪ B) = 12 + 9 + 7 = 28. The common elements must be included once in the union.

Tags

setscardinalityunionintersectionvenn-diagramOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

28

Why is this the correct answer?

The union is divided into three disjoint regions: elements only in A, counted by n(A − B) = 12; elements only in B, counted by n(B − A) = 9; and common elements, counted by n(A ∩ B) = 7. Therefore n(A ∪ B) = 12 + 9 + 7 = 28. The common elements must be included once in 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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