If U = {x ∈ ℤ : −2 ≤ x ≤ 2} and A = {−1, 0, 1}, find A′, the complement of A with respect to U.
Answer and explanation
Correct answer: A′ = {−2, 2} (complement
First list every integer in the universal set: U = {−2, −1, 0, 1, 2}. The complement A′ contains exactly those elements of U that are not present in A. Since A = {−1, 0, 1}, removing these three elements from U leaves −2 and 2. Therefore, A′ = {−2, 2}. The complement is always defined relative to the stated universal set.
Frequently asked questions
What is the correct answer to this question?
A′ = {−2, 2} (complement
Why is this the correct answer?
First list every integer in the universal set: U = {−2, −1, 0, 1, 2}. The complement A′ contains exactly those elements of U that are not present in A. Since A = {−1, 0, 1}, removing these three elements from U leaves −2 and 2. Therefore, A′ = {−2, 2}. The complement is always defined relative to the stated universal set.
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.
