If n(A) = 36, n(B) = 28, and n(A ∩ B) = 12, what is n(A ∪ B)?
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Answer and explanation
Correct answer: 52
For two finite sets, the union formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The intersection is subtracted once because its elements are included in both n(A) and n(B), so they would otherwise be counted twice. Substituting the values gives n(A ∪ B) = 36 + 28 − 12 = 52. Therefore option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
52
Why is this the correct answer?
For two finite sets, the union formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The intersection is subtracted once because its elements are included in both n(A) and n(B), so they would otherwise be counted twice. Substituting the values gives n(A ∪ B) = 36 + 28 − 12 = 52. Therefore option A is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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