In a Venn diagram, n(U) = 210, n(A) = 96, n(B) = 88, and n((A ∪ B)ᶜ) = 58. What is n(A ∩ B)?
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Answer and explanation
Correct answer: 32
The complement (A ∪ B)ᶜ represents the elements in the universal set that are outside both A and B. Thus, n(A ∪ B) = n(U) − n((A ∪ B)ᶜ) = 210 − 58 = 152. For two sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Therefore, 152 = 96 + 88 − n(A ∩ B), which gives n(A ∩ B) = 32. Hence, option C is correct.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
The complement (A ∪ B)ᶜ represents the elements in the universal set that are outside both A and B. Thus, n(A ∪ B) = n(U) − n((A ∪ B)ᶜ) = 210 − 58 = 152. For two sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Therefore, 152 = 96 + 88 − n(A ∩ B), which gives n(A ∩ B) = 32. Hence, option C 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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