If n(A) = 32, n(A ∪ B) = 48, and n(A ∩ B) = 10, what is n(B)?
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Answer and explanation
Correct answer: 26
For two finite sets, the inclusion–exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the data gives 48 = 32 + n(B) − 10 = 22 + n(B). Thus n(B) = 48 − 22 = 26, so option B is correct. The intersection is subtracted because it was counted twice.
Frequently asked questions
What is the correct answer to this question?
26
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 data gives 48 = 32 + n(B) − 10 = 22 + n(B). Thus n(B) = 48 − 22 = 26, so option B is correct. The intersection is subtracted because it was counted twice.
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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