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If n(A) = 18, n(B) = 20, and n(A ∩ B) = 6, what is n(A ∪ B)?
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Answer and explanation
Correct answer: 32
For two finite sets, the union formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The common six elements are included in both n(A) and n(B), so they must be subtracted once to remove double counting. Substituting the values gives 18 + 20 − 6 = 32. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
32
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 common six elements are included in both n(A) and n(B), so they must be subtracted once to remove double counting. Substituting the values gives 18 + 20 − 6 = 32. 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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