If A ⊆ B, n(A) = 52, n(B) = 91 and n(U) = 140, then what is n((B − A) ∪ B')?
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Answer and explanation
Correct answer: 88
Because A is a subset of B, the set B − A contains the elements of B that are not in A, so its size is 91 − 52 = 39. The complement B' contains elements outside B, so n(B') = 140 − 91 = 49. These two regions are disjoint, because one is inside B and the other is outside B. Therefore the required size is 39 + 49 = 88.
Frequently asked questions
What is the correct answer to this question?
88
Why is this the correct answer?
Because A is a subset of B, the set B − A contains the elements of B that are not in A, so its size is 91 − 52 = 39. The complement B' contains elements outside B, so n(B') = 140 − 91 = 49. These two regions are disjoint, because one is inside B and the other is outside B. Therefore the required size is 39 + 49 = 88.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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