If U = {x ∈ ℤ | −5 ≤ x ≤ 5} and A = {x ∈ U | x² < 10}, find A′, the complement of A with respect to U.
Answer and explanation
Correct answer: A′ = {−5, −4, 4, 5}
The universal set is U = {−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5}. The condition x² < 10 means |x| < √10. Since 3 < √10 < 4 and x must be an integer, the possible values are −3 through 3, so A = {−3, −2, −1, 0, 1, 2, 3}. The complement contains every element of U that is not in A. Therefore, A′ = U \ A = {−5, −4, 4, 5}.
Frequently asked questions
What is the correct answer to this question?
A′ = {−5, −4, 4, 5}
Why is this the correct answer?
The universal set is U = {−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5}. The condition x² < 10 means |x| < √10. Since 3 < √10 < 4 and x must be an integer, the possible values are −3 through 3, so A = {−3, −2, −1, 0, 1, 2, 3}. The complement contains every element of U that is not in A. Therefore, A′ = U \ A = {−5, −4, 4, 5}.
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.
