If A ∩ B = ∅, n(A) = 41, n(B) = 39, and n(U) = 100, what is n((A ∪ B)′)?
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Answer and explanation
Correct answer: 20
Since A ∩ B = ∅, the sets A and B are disjoint, so they have no common elements. Thus, n(A ∪ B) = n(A) + n(B) = 41 + 39 = 80. The complement of A ∪ B contains all elements of the universal set that are outside both A and B. Therefore, n((A ∪ B)′) = n(U) − n(A ∪ B) = 100 − 80 = 20. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
Since A ∩ B = ∅, the sets A and B are disjoint, so they have no common elements. Thus, n(A ∪ B) = n(A) + n(B) = 41 + 39 = 80. The complement of A ∪ B contains all elements of the universal set that are outside both A and B. Therefore, n((A ∪ B)′) = n(U) − n(A ∪ B) = 100 − 80 = 20. 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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