If n(Aᶜ) = 48 and n(U) = 95, what is n(A)?
Advertisement
Answer and explanation
Correct answer: 47
The complement Aᶜ contains all elements of the universal set U that are not in A. The sets A and Aᶜ are disjoint and together make up U, so n(A) + n(Aᶜ) = n(U). Substituting the given values gives n(A) + 48 = 95, hence n(A) = 95 − 48 = 47. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
47
Why is this the correct answer?
The complement Aᶜ contains all elements of the universal set U that are not in A. The sets A and Aᶜ are disjoint and together make up U, so n(A) + n(Aᶜ) = n(U). Substituting the given values gives n(A) + 48 = 95, hence n(A) = 95 − 48 = 47. Therefore, option A is correct.
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