If only A has 12, only B has 15, only C has 18, only A ∩ B has 9, only B ∩ C has 7, only C ∩ A has 6, and A ∩ B ∩ C has 4, what is n(A ∩ (B ∪ C))?
Answer and explanation
Correct answer: 19
By the distributive law, A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C). In the Venn diagram this includes the A-B-only region with 9 elements, the A-C-only region with 6 elements, and the central triple-overlap region with 4 elements. These regions are disjoint, so the total is 9 + 6 + 4 = 19. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
19
Why is this the correct answer?
By the distributive law, A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C). In the Venn diagram this includes the A-B-only region with 9 elements, the A-C-only region with 6 elements, and the central triple-overlap region with 4 elements. These regions are disjoint, so the total is 9 + 6 + 4 = 19. 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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