If n(A ∪ B) = 126, n(A − B) = 48, and n(B − A) = 41, then what is n(A ∩ B)?
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Answer and explanation
Correct answer: 37
The union A ∪ B consists of three disjoint Venn 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, 126 = 48 + 41 + n(A ∩ B). Thus n(A ∩ B) = 126 − 48 − 41 = 37. Each region is counted exactly once in this decomposition.
Frequently asked questions
What is the correct answer to this question?
37
Why is this the correct answer?
The union A ∪ B consists of three disjoint Venn 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, 126 = 48 + 41 + n(A ∩ B). Thus n(A ∩ B) = 126 − 48 − 41 = 37. Each region is counted exactly once in this decomposition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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