If A ∩ B = ∅, n(A) = 57, n(B) = 46, and n(U) = 125, what is n((A ∪ B)′)?
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Answer and explanation
Correct answer: 22
Since A ∩ B = ∅, the sets are disjoint and have no common elements. Therefore, n(A ∪ B) = n(A) + n(B) = 57 + 46 = 103. The complement of A ∪ B contains all universal-set elements outside that union. Hence n((A ∪ B)′) = n(U) − n(A ∪ B) = 125 − 103 = 22, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
Since A ∩ B = ∅, the sets are disjoint and have no common elements. Therefore, n(A ∪ B) = n(A) + n(B) = 57 + 46 = 103. The complement of A ∪ B contains all universal-set elements outside that union. Hence n((A ∪ B)′) = n(U) − n(A ∪ B) = 125 − 103 = 22, so 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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