If n(A ∪ B) = 148, n(A − B) = 52, and n(B − A) = 43, what is n(A ∩ B)?
Answer and explanation
Correct answer: 53
The union A ∪ B is divided into three disjoint parts: the elements only in A, the elements only in B, and the elements common to both sets. Hence, 148 = 52 + 43 + n(A ∩ B). Therefore, n(A ∩ B) = 148 − 52 − 43 = 53. The values 52 and 43 must each be subtracted once because they represent non-overlapping exclusive regions. Thus, option C is correct.
Frequently asked questions
What is the correct answer to this question?
53
Why is this the correct answer?
The union A ∪ B is divided into three disjoint parts: the elements only in A, the elements only in B, and the elements common to both sets. Hence, 148 = 52 + 43 + n(A ∩ B). Therefore, n(A ∩ B) = 148 − 52 − 43 = 53. The values 52 and 43 must each be subtracted once because they represent non-overlapping exclusive regions. Thus, option C is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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