If G₂ = {x ∈ ℤ : x² ≤ 1}, which is the correct roster form of G₂?
Answer and explanation
Correct answer: {−1, 0, 1}
For integer x, the inequality x² ≤ 1 means that the absolute value of x is at most 1, or −1 ≤ x ≤ 1. The integers in this interval are −1, 0, and 1. Directly checking confirms that (−1)² = 1, 0² = 0, and 1² = 1, all of which satisfy the inequality. The integers −2 and 2 have square 4 and are excluded. Hence G₂ = {−1, 0, 1}, so A is correct.
Frequently asked questions
What is the correct answer to this question?
{−1, 0, 1}
Why is this the correct answer?
For integer x, the inequality x² ≤ 1 means that the absolute value of x is at most 1, or −1 ≤ x ≤ 1. The integers in this interval are −1, 0, and 1. Directly checking confirms that (−1)² = 1, 0² = 0, and 1² = 1, all of which satisfy the inequality. The integers −2 and 2 have square 4 and are excluded. Hence G₂ = {−1, 0, 1}, so 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.
