If n(A) = 52, n(B) = 47, n(A ∩ B) = 21, and n(U) = 80, what is n((A ∪ B)')?
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Answer and explanation
Correct answer: 2
First apply the inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 52 + 47 − 21 = 78. The complement (A ∪ B)' contains the elements of the universal set that are in neither A nor B. Therefore, n((A ∪ B)') = n(U) − n(A ∪ B) = 80 − 78 = 2. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
First apply the inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 52 + 47 − 21 = 78. The complement (A ∪ B)' contains the elements of the universal set that are in neither A nor B. Therefore, n((A ∪ B)') = n(U) − n(A ∪ B) = 80 − 78 = 2. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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