If n(A ∪ B) = 81, the number of elements only in A is 29, and the number only in B is 34, what is n(A ∩ B)?
Answer and explanation
Correct answer: 18
The union is divided into three non-overlapping regions: only A, the intersection A ∩ B, and only B. Thus, n(A ∪ B) = 29 + n(A ∩ B) + 34. Rearranging gives n(A ∩ B) = 81 − 29 − 34 = 18. Therefore, option A is correct. The values 29 and 34 are exclusive regions, so they must be subtracted from the union.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The union is divided into three non-overlapping regions: only A, the intersection A ∩ B, and only B. Thus, n(A ∪ B) = 29 + n(A ∩ B) + 34. Rearranging gives n(A ∩ B) = 81 − 29 − 34 = 18. Therefore, option A is correct. The values 29 and 34 are exclusive regions, so they must be subtracted from the union.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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