Which is the roster form of D = {x ∈ ℤ : |x − 2| ≤ 3}?
Answer and explanation
Correct answer: D = {−1, 0, 1, 2, 3, 4, 5}
The condition |x − 2| ≤ 3 means that x is at a distance of at most 3 from 2. Therefore, subtracting and adding 3 gives −1 ≤ x ≤ 5. Since x must be an integer, we list every integer in this closed interval: −1, 0, 1, 2, 3, 4, and 5. Hence the roster form is D = {−1, 0, 1, 2, 3, 4, 5}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
D = {−1, 0, 1, 2, 3, 4, 5}
Why is this the correct answer?
The condition |x − 2| ≤ 3 means that x is at a distance of at most 3 from 2. Therefore, subtracting and adding 3 gives −1 ≤ x ≤ 5. Since x must be an integer, we list every integer in this closed interval: −1, 0, 1, 2, 3, 4, and 5. Hence the roster form is D = {−1, 0, 1, 2, 3, 4, 5}, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
