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

If n(A) = 45, n(B) = 38, and only A has 19 elements, that is, n(A − B) = 19, what is n(A ∩ B)?

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Answer and explanation

Correct answer: 26

Set A is divided into two disjoint parts: the elements only in A, represented by A − B, and the elements common to A and B, represented by A ∩ B. Therefore n(A) = n(A − B) + n(A ∩ B). Using the given values, 45 = 19 + n(A ∩ B), so n(A ∩ B) = 45 − 19 = 26. Hence option B is the only correct answer.

Tags

setsvenn-diagramsintersectionset-differenceOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

26

Why is this the correct answer?

Set A is divided into two disjoint parts: the elements only in A, represented by A − B, and the elements common to A and B, represented by A ∩ B. Therefore n(A) = n(A − B) + n(A ∩ B). Using the given values, 45 = 19 + n(A ∩ B), so n(A ∩ B) = 45 − 19 = 26. Hence option B is the only correct answer.

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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