If n(A ∪ B) = 128, n(A ∩ B) = 32, and n(A − B) = 45, what is n(B)?
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Answer and explanation
Correct answer: 83
The union A ∪ B consists of three disjoint regions: elements only in A, elements common to A and B, and elements only in B. Since n(A − B) = 45 and n(A ∩ B) = 32, the number of elements only in B is 128 − 45 − 32 = 51. Therefore, n(B) = n(B − A) + n(A ∩ B) = 51 + 32 = 83. Hence, option C is correct.
Frequently asked questions
What is the correct answer to this question?
83
Why is this the correct answer?
The union A ∪ B consists of three disjoint regions: elements only in A, elements common to A and B, and elements only in B. Since n(A − B) = 45 and n(A ∩ B) = 32, the number of elements only in B is 128 − 45 − 32 = 51. Therefore, n(B) = n(B − A) + n(A ∩ B) = 51 + 32 = 83. Hence, option C 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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