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

If n(A) = 14, n(B) = 9, and n(A ∩ B) = 4, what is n(A ∪ B)?

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Answer and explanation

Correct answer: 19

Use the inclusion–exclusion formula for two finite sets: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 14 + 9 − 4 = 19. The intersection is subtracted because its four elements were counted once in n(A) and again in n(B). Therefore option A, 19, is correct.

Tags

setscardinalityunioninclusion-exclusionOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

19

Why is this the correct answer?

Use the inclusion–exclusion formula for two finite sets: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 14 + 9 − 4 = 19. The intersection is subtracted because its four elements were counted once in n(A) and again in n(B). Therefore option A, 19, 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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