In a Venn diagram, n(A ∩ B) = 0 and n(A ∪ B) = 92. If n(A) = 40, what is n(B)?
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Answer and explanation
Correct answer: 52
The general formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Since n(A ∩ B) = 0, the sets are disjoint and the formula becomes 92 = 40 + n(B). Thus n(B) = 92 − 40 = 52. Option A merely repeats n(A), while option C is the union total, not the size of B. Therefore, B is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
52
Why is this the correct answer?
The general formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Since n(A ∩ B) = 0, the sets are disjoint and the formula becomes 92 = 40 + n(B). Thus n(B) = 92 − 40 = 52. Option A merely repeats n(A), while option C is the union total, not the size of B. Therefore, B is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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