If U = {1, 2, 3, …, 16} and A is the set of perfect squares in U, how many elements does Aᶜ contain?
Answer and explanation
Correct answer: 12
The perfect squares in U = {1, 2, 3, …, 16} are 1, 4, 9, and 16, so A contains 4 elements. The universal set contains 16 elements altogether. Therefore the complement contains the remaining elements: n(Aᶜ) = n(U) − n(A) = 16 − 4 = 12. Hence option C is correct. Option A is n(A), and option D is the size of U, not its complement.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The perfect squares in U = {1, 2, 3, …, 16} are 1, 4, 9, and 16, so A contains 4 elements. The universal set contains 16 elements altogether. Therefore the complement contains the remaining elements: n(Aᶜ) = n(U) − n(A) = 16 − 4 = 12. Hence option C is correct. Option A is n(A), and option D is the size of U, 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.
