In a survey, n(U) = 120, n(A) = 62, n(B) = 55, and n(A ∪ B) = 91. According to the Venn diagram, what is n(A ∩ B)?
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Answer and explanation
Correct answer: 26
For two finite sets, the addition n(A) + n(B) counts the common elements twice, so the union formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Rearranging gives n(A ∩ B) = n(A) + n(B) − n(A ∪ B) = 62 + 55 − 91 = 26. The universal-set size is not required because the union size is already supplied.
Frequently asked questions
What is the correct answer to this question?
26
Why is this the correct answer?
For two finite sets, the addition n(A) + n(B) counts the common elements twice, so the union formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Rearranging gives n(A ∩ B) = n(A) + n(B) − n(A ∪ B) = 62 + 55 − 91 = 26. The universal-set size is not required because the union size is already supplied.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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