If n(A ∪ B) = 73, n(A − B) = 28, and n(B − A) = 32, which statement is correct?
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Answer and explanation
Correct answer: n(A ∩ B) = 13
In a two-set Venn diagram, the union is the disjoint sum of the A-only region, the B-only region, and the common region. Thus n(A∪B) = n(A−B)+n(B−A)+n(A∩B). Substituting gives 73 = 28+32+n(A∩B), so n(A∩B) = 73−60 = 13. The value 60 is only the sum of the exclusive regions; therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
n(A ∩ B) = 13
Why is this the correct answer?
In a two-set Venn diagram, the union is the disjoint sum of the A-only region, the B-only region, and the common region. Thus n(A∪B) = n(A−B)+n(B−A)+n(A∩B). Substituting gives 73 = 28+32+n(A∩B), so n(A∩B) = 73−60 = 13. The value 60 is only the sum of the exclusive regions; therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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