Which is the roster form of A₁ = {x : x ∈ ℤ and |x| < 3}?
Answer and explanation
Correct answer: A₁ = {−2, −1, 0, 1, 2}
The inequality |x| < 3 means that x lies within a distance of less than 3 from zero. Equivalently, −3 < x < 3. The integers strictly between −3 and 3 are −2, −1, 0, 1, and 2. The endpoints −3 and 3 are excluded because the inequality is strict. Therefore, the roster form is given in option A.
Frequently asked questions
What is the correct answer to this question?
A₁ = {−2, −1, 0, 1, 2}
Why is this the correct answer?
The inequality |x| < 3 means that x lies within a distance of less than 3 from zero. Equivalently, −3 < x < 3. The integers strictly between −3 and 3 are −2, −1, 0, 1, and 2. The endpoints −3 and 3 are excluded because the inequality is strict. Therefore, the roster form is given in option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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