If A = {x ∈ Z : −3 ≤ x ≤ 2} and B = {x ∈ Z : x² ≤ 4}, what is A ∪ B?
Answer and explanation
Correct answer: {−3, −2, −1, 0, 1, 2}
Because x is an integer and −3 ≤ x ≤ 2, A = {−3, −2, −1, 0, 1, 2}. The condition x² ≤ 4 means −2 ≤ x ≤ 2, so B = {−2, −1, 0, 1, 2}. Every element of B is already in A. Therefore their union contains all distinct elements of A and B, which is A ∪ B = {−3, −2, −1, 0, 1, 2}. Option B gives only B, not the union.
Frequently asked questions
What is the correct answer to this question?
{−3, −2, −1, 0, 1, 2}
Why is this the correct answer?
Because x is an integer and −3 ≤ x ≤ 2, A = {−3, −2, −1, 0, 1, 2}. The condition x² ≤ 4 means −2 ≤ x ≤ 2, so B = {−2, −1, 0, 1, 2}. Every element of B is already in A. Therefore their union contains all distinct elements of A and B, which is A ∪ B = {−3, −2, −1, 0, 1, 2}. Option B gives only B, not the union.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
