If n(A) = 46, n(B) = 35, and n(B \ A) = 24, what is n(A ∩ B)?
Answer and explanation
Correct answer: 11
The set B is the disjoint union of B \ A and A ∩ B: every element of B is either outside A or common to both sets. Therefore n(B) = n(B \ A) + n(A ∩ B). Using n(B) = 35 and n(B \ A) = 24, we get 35 = 24 + n(A ∩ B), so n(A ∩ B) = 11. Option A is correct. The value 24 describes only B \ A, not the intersection.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
The set B is the disjoint union of B \ A and A ∩ B: every element of B is either outside A or common to both sets. Therefore n(B) = n(B \ A) + n(A ∩ B). Using n(B) = 35 and n(B \ A) = 24, we get 35 = 24 + n(A ∩ B), so n(A ∩ B) = 11. Option A is correct. The value 24 describes only B \ A, not the intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
