If n(A) = 48, n(B) = 52, n(A − B) = 17, and n(B − A) = 21, what is n(A ∩ B)?
Answer and explanation
Correct answer: 31
The set A is divided into two disjoint parts: A − B and A ∩ B. Therefore n(A) = n(A − B) + n(A ∩ B). Substituting the given values gives 48 = 17 + n(A ∩ B), so n(A ∩ B) = 31. This is confirmed independently from B: 52 − 21 = 31. Thus option A is correct; the other values result from subtracting the wrong region or adding unrelated parts.
Frequently asked questions
What is the correct answer to this question?
31
Why is this the correct answer?
The set A is divided into two disjoint parts: A − B and A ∩ B. Therefore n(A) = n(A − B) + n(A ∩ B). Substituting the given values gives 48 = 17 + n(A ∩ B), so n(A ∩ B) = 31. This is confirmed independently from B: 52 − 21 = 31. Thus option A is correct; the other values result from subtracting the wrong region or adding unrelated parts.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
