If n(A ∪ B) = 76, n(A − B) = 31, and n(B − A) = 27, what is n(A ∩ B)?
Answer and explanation
Correct answer: 18
The union A ∪ B consists of three mutually disjoint regions: the elements only in A, the elements only in B, and the elements common to both sets. Therefore, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the given values gives 76 = 31 + 27 + n(A ∩ B), so n(A ∩ B) = 18. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The union A ∪ B consists of three mutually disjoint regions: the elements only in A, the elements only in B, and the elements common to both sets. Therefore, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the given values gives 76 = 31 + 27 + n(A ∩ B), so n(A ∩ B) = 18. Hence, option A is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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