If n(A) = 13, n(B) = 17, and n(A ∩ B) = 5, what is n(A ∪ B)?
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Answer and explanation
Correct answer: 25
For two finite sets, the inclusion–exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The intersection is counted in both n(A) and n(B), so it must be subtracted once to prevent double counting. Thus, n(A ∪ B) = 13 + 17 − 5 = 25. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
For two finite sets, the inclusion–exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The intersection is counted in both n(A) and n(B), so it must be subtracted once to prevent double counting. Thus, n(A ∪ B) = 13 + 17 − 5 = 25. Therefore, option A 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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