If A ∩ B = ∅, n(A) = 44, n(B) = 52, and n(U) = 130, what is n((A ∪ B)′)?
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Answer and explanation
Correct answer: 34
Since A and B are disjoint, they have no common elements, so n(A ∪ B) = n(A) + n(B) = 44 + 52 = 96. The complement of A ∪ B contains all elements of the universal set U that are outside the union. Thus, n((A ∪ B)′) = n(U) − n(A ∪ B) = 130 − 96 = 34. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
34
Why is this the correct answer?
Since A and B are disjoint, they have no common elements, so n(A ∪ B) = n(A) + n(B) = 44 + 52 = 96. The complement of A ∪ B contains all elements of the universal set U that are outside the union. Thus, n((A ∪ B)′) = n(U) − n(A ∪ B) = 130 − 96 = 34. Therefore, 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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