If n(A′) = 35, n(B′) = 42, n(U) = 80, and n(A ∩ B) = 25, what is n(A′ ∩ B′)?
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Answer and explanation
Correct answer: 22
First find the sizes of A and B from their complements: n(A) = 80 − 35 = 45 and n(B) = 80 − 42 = 38. Then n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 45 + 38 − 25 = 58. Since A′ ∩ B′ = (A ∪ B)′ by De Morgan’s law, n(A′ ∩ B′) = 80 − 58 = 22. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
First find the sizes of A and B from their complements: n(A) = 80 − 35 = 45 and n(B) = 80 − 42 = 38. Then n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 45 + 38 − 25 = 58. Since A′ ∩ B′ = (A ∪ B)′ by De Morgan’s law, n(A′ ∩ B′) = 80 − 58 = 22. Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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