If n(A ∩ B′) = 18, n(A′ ∩ B) = 22, n(A ∩ B) = 16, and n(U) = 75, what is n(A′ ∩ B′)?
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Answer and explanation
Correct answer: 19
A universal set divided by A and B has four disjoint regions: A ∩ B′, A′ ∩ B, A ∩ B, and A′ ∩ B′. The first three contain 18, 22, and 16 elements, so their total is 56. Since the universal set has 75 elements, the outside region is 75 − 56 = 19. Therefore, n(A′ ∩ B′) = 19.
Frequently asked questions
What is the correct answer to this question?
19
Why is this the correct answer?
A universal set divided by A and B has four disjoint regions: A ∩ B′, A′ ∩ B, A ∩ B, and A′ ∩ B′. The first three contain 18, 22, and 16 elements, so their total is 56. Since the universal set has 75 elements, the outside region is 75 − 56 = 19. Therefore, n(A′ ∩ B′) = 19.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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