In a Venn diagram, n(A) = 91, n(B) = 87, and n(A ∩ B) = 34. If n(U) = 190, what is n((A ∪ B)ᶜ)?
Advertisement
Answer and explanation
Correct answer: 46
First calculate the union using the addition rule for two sets: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 91 + 87 − 34 = 144. The complement of A ∪ B consists of elements in the universal set that belong to neither A nor B. Hence n((A ∪ B)ᶜ) = n(U) − n(A ∪ B) = 190 − 144 = 46. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
46
Why is this the correct answer?
First calculate the union using the addition rule for two sets: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 91 + 87 − 34 = 144. The complement of A ∪ B consists of elements in the universal set that belong to neither A nor B. Hence n((A ∪ B)ᶜ) = n(U) − n(A ∪ B) = 190 − 144 = 46. 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.
Advertisement