If n(A ∪ B) = 88, n(A − B) = 31, and n(B − A) = 29, what is n(A ∩ B)?
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Answer and explanation
Correct answer: 28
The union A ∪ B is divided into three mutually exclusive Venn-diagram regions: A − B, B − A, and A ∩ B. Therefore, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the given values gives 88 = 31 + 29 + n(A ∩ B), so n(A ∩ B) = 88 − 60 = 28. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
28
Why is this the correct answer?
The union A ∪ B is divided into three mutually exclusive Venn-diagram regions: A − B, B − A, and A ∩ B. Therefore, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the given values gives 88 = 31 + 29 + n(A ∩ B), so n(A ∩ B) = 88 − 60 = 28. Hence option B 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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