If n(A∩Bᶜ)=41, n(Aᶜ∩B)=34, n(A∩B)=26, and n(U)=130, what is n(Aᶜ∩Bᶜ)?
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Answer and explanation
Correct answer: 29
A two-set Venn diagram divides the universal set into four disjoint regions: A∩Bᶜ, Aᶜ∩B, A∩B, and Aᶜ∩Bᶜ. The first three regions contain 41+34+26=101 elements. Since all four regions together contain 130 elements, the remaining region is n(Aᶜ∩Bᶜ)=130−101=29. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
29
Why is this the correct answer?
A two-set Venn diagram divides the universal set into four disjoint regions: A∩Bᶜ, Aᶜ∩B, A∩B, and Aᶜ∩Bᶜ. The first three regions contain 41+34+26=101 elements. Since all four regions together contain 130 elements, the remaining region is n(Aᶜ∩Bᶜ)=130−101=29. 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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