If U = {x : x ∈ ℤ, −10 ≤ x ≤ 10} and A = {x : x ∈ U and |x| ≤ 3}, what is n(A')?
Answer and explanation
Correct answer: 14
The universal set U contains all integers from −10 through 10, including both endpoints, so n(U) = 10 − (−10) + 1 = 21. The condition |x| ≤ 3 means −3 ≤ x ≤ 3, giving A = {−3, −2, −1, 0, 1, 2, 3}, which has 7 elements. Since A' contains the elements of U that are not in A, n(A') = n(U) − n(A) = 21 − 7 = 14. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
The universal set U contains all integers from −10 through 10, including both endpoints, so n(U) = 10 − (−10) + 1 = 21. The condition |x| ≤ 3 means −3 ≤ x ≤ 3, giving A = {−3, −2, −1, 0, 1, 2, 3}, which has 7 elements. Since A' contains the elements of U that are not in A, n(A') = n(U) − n(A) = 21 − 7 = 14. 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.
