If n(A∪B)=63, only A is 24, and only B is 27, what is n(A∩B)?
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Answer and explanation
Correct answer: 12
A two-set Venn diagram divides A ∪ B into three disjoint regions: only A, A ∩ B, and only B. Their counts must add to the union total. Therefore 63 = 24 + n(A ∩ B) + 27, so n(A ∩ B) = 63 − 24 − 27 = 12. Option A is correct. The numbers 24 and 27 are separate-only regions, not the common region.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
A two-set Venn diagram divides A ∪ B into three disjoint regions: only A, A ∩ B, and only B. Their counts must add to the union total. Therefore 63 = 24 + n(A ∩ B) + 27, so n(A ∩ B) = 63 − 24 − 27 = 12. Option A is correct. The numbers 24 and 27 are separate-only regions, not the common region.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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