Let U = Z and A = {x ∈ Z : −2 ≤ x ≤ 3}. Which is the correct description of A′?
Answer and explanation
Correct answer: {x ∈ Z : x < −2 or x > 3}
Because the universal set is all integers, A contains every integer from −2 through 3, including both endpoints: {−2,−1,0,1,2,3}. Its complement therefore contains all integers outside this closed interval. In set-builder form, A′ = {x ∈ Z : x < −2 or x > 3}; the endpoints are excluded from the complement.
Frequently asked questions
What is the correct answer to this question?
{x ∈ Z : x < −2 or x > 3}
Why is this the correct answer?
Because the universal set is all integers, A contains every integer from −2 through 3, including both endpoints: {−2,−1,0,1,2,3}. Its complement therefore contains all integers outside this closed interval. In set-builder form, A′ = {x ∈ Z : x < −2 or x > 3}; the endpoints are excluded from the 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.
