If n(U) = 110, n(A) = 58, n(B) = 49 and n(A − B) = 21, then what is n((A ∪ B)′)?
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Answer and explanation
Correct answer: 40
The set A consists of the part only in A and the common part. Therefore, n(A ∩ B) = n(A) − n(A − B) = 58 − 21 = 37. Then n(A ∪ B) = 58 + 49 − 37 = 70. The complement contains the elements of U outside this union, so n((A ∪ B)′) = 110 − 70 = 40. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
The set A consists of the part only in A and the common part. Therefore, n(A ∩ B) = n(A) − n(A − B) = 58 − 21 = 37. Then n(A ∪ B) = 58 + 49 − 37 = 70. The complement contains the elements of U outside this union, so n((A ∪ B)′) = 110 − 70 = 40. Option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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