If n(U)=130 and n(A∩B)=46, what is n((A∩B)ᶜ)?
Advertisement
Answer and explanation
Correct answer: 84
The complement of A∩B is taken with respect to the universal set U. It contains every element of U that is not in the common part A∩B. For a finite universal set, n(Xᶜ)=n(U)−n(X). Hence n((A∩B)ᶜ)=130−46=84. Therefore option B is correct; the intersection itself has 46 elements, not its complement.
Frequently asked questions
What is the correct answer to this question?
84
Why is this the correct answer?
The complement of A∩B is taken with respect to the universal set U. It contains every element of U that is not in the common part A∩B. For a finite universal set, n(Xᶜ)=n(U)−n(X). Hence n((A∩B)ᶜ)=130−46=84. Therefore option B is correct; the intersection itself has 46 elements, not its complement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
Advertisement