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

If n(A) = 18, n(B) = 22, and n(A ∪ B) = 31, what is n(A \ B)?

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Answer and explanation

Correct answer: 9

Use the inclusion–exclusion formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Thus, 31 = 18 + 22 − n(A ∩ B), so n(A ∩ B) = 9. The difference A \ B contains the elements of A that are not in B, so n(A \ B) = n(A) − n(A ∩ B) = 18 − 9 = 9. Therefore, option A is correct.

Tags

setscardinalityinclusion-exclusiondifferencecountingOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

9

Why is this the correct answer?

Use the inclusion–exclusion formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Thus, 31 = 18 + 22 − n(A ∩ B), so n(A ∩ B) = 9. The difference A \ B contains the elements of A that are not in B, so n(A \ B) = n(A) − n(A ∩ B) = 18 − 9 = 9. Therefore, 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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