In a Venn diagram, n(U) = 180, n(A) = 92, n(B) = 84, and n((A ∪ B)ᶜ) = 38. What is n(A ∩ B)?
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Answer and explanation
Correct answer: 34
The complement of A ∪ B contains elements outside both sets. Thus, n(A ∪ B) = n(U) − n((A ∪ B)ᶜ) = 180 − 38 = 142. For two sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the values gives 142 = 92 + 84 − n(A ∩ B), so n(A ∩ B) = 176 − 142 = 34. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
34
Why is this the correct answer?
The complement of A ∪ B contains elements outside both sets. Thus, n(A ∪ B) = n(U) − n((A ∪ B)ᶜ) = 180 − 38 = 142. For two sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the values gives 142 = 92 + 84 − n(A ∩ B), so n(A ∩ B) = 176 − 142 = 34. Therefore, option B 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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