If n(A ∪ B) = 136, n(A − B) = 49, and n(A ∩ B) = 31, what is n(B)?
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Answer and explanation
Correct answer: 87
The union is divided into three disjoint regions: A − B, A ∩ B, and B − A. First, n(B − A) = 136 − 49 − 31 = 56. Set B consists of B − A together with A ∩ B, so n(B) = 56 + 31 = 87. Therefore, option C is correct; 56 counts only the non-common part of B.
Frequently asked questions
What is the correct answer to this question?
87
Why is this the correct answer?
The union is divided into three disjoint regions: A − B, A ∩ B, and B − A. First, n(B − A) = 136 − 49 − 31 = 56. Set B consists of B − A together with A ∩ B, so n(B) = 56 + 31 = 87. Therefore, option C is correct; 56 counts only the non-common part of B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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