If n(B) = 42 and n(B \ A) = 25, what is n(A ∩ B)?
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Answer and explanation
Correct answer: 17
The set B is divided into two disjoint parts: B \ A, which contains elements of B outside A, and A ∩ B, which contains elements common to A and B. Thus n(B) = n(B \ A) + n(A ∩ B). Consequently, 42 = 25 + n(A ∩ B), giving n(A ∩ B) = 17. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
The set B is divided into two disjoint parts: B \ A, which contains elements of B outside A, and A ∩ B, which contains elements common to A and B. Thus n(B) = n(B \ A) + n(A ∩ B). Consequently, 42 = 25 + n(A ∩ B), giving n(A ∩ B) = 17. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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