If n(U) = 110, n(A) = 58, n(B) = 49, and n(A − B) = 21, choose the correct value of n((A ∪ B)′).
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Answer and explanation
Correct answer: 40
The set A contains its exclusive part A − B and its common part A ∩ B. Hence, n(A ∩ B) = n(A) − n(A − B) = 58 − 21 = 37. Using the inclusion–exclusion formula, n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 58 + 49 − 37 = 70. Therefore, the complement has 110 − 70 = 40 elements. Thus, 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 contains its exclusive part A − B and its common part A ∩ B. Hence, n(A ∩ B) = n(A) − n(A − B) = 58 − 21 = 37. Using the inclusion–exclusion formula, n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 58 + 49 − 37 = 70. Therefore, the complement has 110 − 70 = 40 elements. Thus, 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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