If n(U) = 150, n(A) = 70, n(B) = 65, and n(A ∩ B) = 28, what is n((A ∪ B)')?
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Answer and explanation
Correct answer: 43
The complement of A ∪ B contains elements of the universal set that belong to neither A nor B. First calculate the union using n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 70 + 65 − 28 = 107. Then subtract this union from the universal set: n((A ∪ B)') = n(U) − n(A ∪ B) = 150 − 107 = 43. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
43
Why is this the correct answer?
The complement of A ∪ B contains elements of the universal set that belong to neither A nor B. First calculate the union using n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 70 + 65 − 28 = 107. Then subtract this union from the universal set: n((A ∪ B)') = n(U) − n(A ∪ B) = 150 − 107 = 43. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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