If n(U) = 100, n(A) = 48, n(B) = 52, and n(A′ ∩ B′) = 18, what is n(A ∩ B)?
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Answer and explanation
Correct answer: 18
The region A′ ∩ B′ contains elements outside both A and B. By De Morgan’s law, A′ ∩ B′ = (A ∪ B)′, so n(A ∪ B) = n(U) − n(A′ ∩ B′) = 100 − 18 = 82. Using n(A ∪ B) = n(A) + n(B) − n(A ∩ B), we get 82 = 48 + 52 − n(A ∩ B). Therefore, n(A ∩ B) = 18. Thus, option A is correct.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The region A′ ∩ B′ contains elements outside both A and B. By De Morgan’s law, A′ ∩ B′ = (A ∪ B)′, so n(A ∪ B) = n(U) − n(A′ ∩ B′) = 100 − 18 = 82. Using n(A ∪ B) = n(A) + n(B) − n(A ∩ B), we get 82 = 48 + 52 − n(A ∩ B). Therefore, n(A ∩ B) = 18. Thus, 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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