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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 11

If n(A ∪ B) = 126, n(A − B) = 47, and n(B − A) = 39, what is n(A ∩ B)?

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Answer and explanation

Correct answer: 40

The union A ∪ B is divided into three disjoint regions: the elements only in A, counted by n(A − B) = 47; the elements only in B, counted by n(B − A) = 39; and the common elements, counted by n(A ∩ B). Therefore, 126 = 47 + 39 + n(A ∩ B), so n(A ∩ B) = 126 − 86 = 40. Hence, option A is correct.

Tags

setsoperations on setsunionintersectionvenn diagramsMathematicsOperations on Sets (UnionDifference)operations on sets union intersection difference

Frequently asked questions

What is the correct answer to this question?

40

Why is this the correct answer?

The union A ∪ B is divided into three disjoint regions: the elements only in A, counted by n(A − B) = 47; the elements only in B, counted by n(B − A) = 39; and the common elements, counted by n(A ∩ B). Therefore, 126 = 47 + 39 + n(A ∩ B), so n(A ∩ B) = 126 − 86 = 40. Hence, option A is 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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