For a universal set U, if n(U)=200, n(A′)=76, n(B′)=89, and n(A′∩B′)=31, what is n((A∩B)′)?
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Answer and explanation
Correct answer: 134
De Morgan’s law states that (A∩B)′=A′∪B′. The inclusion–exclusion formula gives n(A′∪B′)=n(A′)+n(B′)−n(A′∩B′). Substituting the given values, we obtain 76+89−31=134. The intersection must be subtracted once because it is counted in both sets. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
134
Why is this the correct answer?
De Morgan’s law states that (A∩B)′=A′∪B′. The inclusion–exclusion formula gives n(A′∪B′)=n(A′)+n(B′)−n(A′∩B′). Substituting the given values, we obtain 76+89−31=134. The intersection must be subtracted once because it is counted in both sets. 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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