If n(A) = 42, n(B) = 35, and n(A ∪ B) = 60, what is n(A ∩ B)?
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Answer and explanation
Correct answer: 17
For two finite sets, the inclusion–exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 60 = 42 + 35 − n(A ∩ B), so 60 = 77 − n(A ∩ B). Therefore, n(A ∩ B) = 77 − 60 = 17. The common elements must be subtracted once because they were counted in both A and B.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
For two finite sets, the inclusion–exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 60 = 42 + 35 − n(A ∩ B), so 60 = 77 − n(A ∩ B). Therefore, n(A ∩ B) = 77 − 60 = 17. The common elements must be subtracted once because they were counted in both A and B.
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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