If O = {x ∈ Z : |x| ≤ 2}, what is the correct roster form of O?
Answer and explanation
Correct answer: O = {-2, -1, 0, 1, 2}
The absolute-value condition |x| ≤ 2 means that x is at a distance of at most 2 from zero. Among the integers, the values satisfying this are −2, −1, 0, 1, and 2. Both endpoints are included because the inequality is less than or equal to, and zero is also an integer satisfying the condition. Therefore, option A gives the correct roster form.
Frequently asked questions
What is the correct answer to this question?
O = {-2, -1, 0, 1, 2}
Why is this the correct answer?
The absolute-value condition |x| ≤ 2 means that x is at a distance of at most 2 from zero. Among the integers, the values satisfying this are −2, −1, 0, 1, and 2. Both endpoints are included because the inequality is less than or equal to, and zero is also an integer satisfying the condition. Therefore, option A gives the correct roster form.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
