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