Which is the correct roster form for the set {x ∈ ℤ : −2 ≤ x ≤ 2}?
Answer and explanation
Correct answer: {−2, −1, 0, 1, 2}
The governing concept is converting set-builder notation into roster form. The symbol ℤ restricts x to integers, and the inclusive inequality −2 ≤ x ≤ 2 includes every integer from −2 through 2. Listing them gives −2, −1, 0, 1, and 2, so the set has five elements and option A is correct. Option B lists only the endpoints, option C omits both endpoints, and option D wrongly treats the set as empty.
Frequently asked questions
What is the correct answer to this question?
{−2, −1, 0, 1, 2}
Why is this the correct answer?
The governing concept is converting set-builder notation into roster form. The symbol ℤ restricts x to integers, and the inclusive inequality −2 ≤ x ≤ 2 includes every integer from −2 through 2. Listing them gives −2, −1, 0, 1, and 2, so the set has five elements and option A is correct. Option B lists only the endpoints, option C omits both endpoints, and option D wrongly treats the set as empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
