If n(U) = 75, n(A) = 28, n(B) = 35, and n(A ∪ B) = 50, what is n((A' ∩ B')')?
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Answer and explanation
Correct answer: 50
By De Morgan’s law, A' ∩ B' = (A ∪ B)'. Taking the complement once more gives (A' ∩ B')' = ((A ∪ B)')' = A ∪ B, using the double-complement law. The question already gives n(A ∪ B) = 50, so n((A' ∩ B')') = 50. The values of n(U), n(A), and n(B) are not needed after this identity is applied.
Frequently asked questions
What is the correct answer to this question?
50
Why is this the correct answer?
By De Morgan’s law, A' ∩ B' = (A ∪ B)'. Taking the complement once more gives (A' ∩ B')' = ((A ∪ B)')' = A ∪ B, using the double-complement law. The question already gives n(A ∪ B) = 50, so n((A' ∩ B')') = 50. The values of n(U), n(A), and n(B) are not needed after this identity is applied.
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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