If n(A ∩ B) = 45, n(A ∩ C) = 38, n(B ∩ C) = 35, and n(A ∩ B ∩ C) = 16, how many elements are in exactly two sets?
Answer and explanation
Correct answer: 70
Each pairwise intersection includes the 16 elements that lie in all three sets. Therefore, the pair-only regions are n(A ∩ B only) = 45 − 16 = 29, n(A ∩ C only) = 38 − 16 = 22, and n(B ∩ C only) = 35 − 16 = 19. These regions are disjoint, so the number in exactly two sets is 29 + 22 + 19 = 70. Option C is correct; adding 45 + 38 + 35 would count the central region repeatedly.
Frequently asked questions
What is the correct answer to this question?
70
Why is this the correct answer?
Each pairwise intersection includes the 16 elements that lie in all three sets. Therefore, the pair-only regions are n(A ∩ B only) = 45 − 16 = 29, n(A ∩ C only) = 38 − 16 = 22, and n(B ∩ C only) = 35 − 16 = 19. These regions are disjoint, so the number in exactly two sets is 29 + 22 + 19 = 70. Option C is correct; adding 45 + 38 + 35 would count the central region repeatedly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
