Which is the roster form of the set C = {x ∈ ℤ : |x − 2| ≤ 1}?
Answer and explanation
Correct answer: C = {1, 2, 3}
The inequality |x − 2| ≤ 1 means that x is at a distance of at most 1 from 2. Equivalently, −1 ≤ x − 2 ≤ 1. Adding 2 throughout gives 1 ≤ x ≤ 3. Since x must be an integer, the possible values are 1, 2 and 3. Thus the correct roster form is C = {1, 2, 3}. The endpoints are included because the inequality is non-strict.
Frequently asked questions
What is the correct answer to this question?
C = {1, 2, 3}
Why is this the correct answer?
The inequality |x − 2| ≤ 1 means that x is at a distance of at most 1 from 2. Equivalently, −1 ≤ x − 2 ≤ 1. Adding 2 throughout gives 1 ≤ x ≤ 3. Since x must be an integer, the possible values are 1, 2 and 3. Thus the correct roster form is C = {1, 2, 3}. The endpoints are included because the inequality is non-strict.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
