If U = {1, 2, 3, …, 15} and A is the set of perfect squares in U, how many elements are in Aᶜ?
Answer and explanation
Correct answer: 12
The perfect squares among the integers from 1 through 15 are 1, 4, and 9, so n(A) = 3. The universal set U has 15 elements. Since Aᶜ contains all elements of U that are not in A, use n(Aᶜ) = n(U) − n(A) = 15 − 3 = 12. Therefore option B is correct. The value 3 is not listed, while 15 ignores the excluded squares.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The perfect squares among the integers from 1 through 15 are 1, 4, and 9, so n(A) = 3. The universal set U has 15 elements. Since Aᶜ contains all elements of U that are not in A, use n(Aᶜ) = n(U) − n(A) = 15 − 3 = 12. Therefore option B is correct. The value 3 is not listed, while 15 ignores the excluded squares.
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.
