If n(U) = 20 and n(A) = 7, what is n(Aᶜ)?
Answer and explanation
Correct answer: 13
For a set A contained in the universal set U, the complement Aᶜ contains every element of U that is not in A. Therefore, the number of elements in the complement is found by subtracting the number of elements of A from the number of elements of U: n(Aᶜ) = n(U) − n(A) = 20 − 7 = 13. Hence, option A is correct. Option C gives n(A), while option D gives n(U), not the complement.
Frequently asked questions
What is the correct answer to this question?
13
Why is this the correct answer?
For a set A contained in the universal set U, the complement Aᶜ contains every element of U that is not in A. Therefore, the number of elements in the complement is found by subtracting the number of elements of A from the number of elements of U: n(Aᶜ) = n(U) − n(A) = 20 − 7 = 13. Hence, option A is correct. Option C gives n(A), while option D gives n(U), not the 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.
