Which set is equal to A = {x ∈ ℤ : |x| < 4}?
Answer and explanation
Correct answer: {−3, −2, −1, 0, 1, 2, 3}
For any real number x, |x| < 4 is equivalent to −4 < x < 4. Since x must be an integer, the possible values are −3, −2, −1, 0, 1, 2, and 3. The endpoints −4 and 4 are excluded because the inequality is strict. Thus A contains exactly the seven integers listed in option A, so that set is equal to A.
Frequently asked questions
What is the correct answer to this question?
{−3, −2, −1, 0, 1, 2, 3}
Why is this the correct answer?
For any real number x, |x| < 4 is equivalent to −4 < x < 4. Since x must be an integer, the possible values are −3, −2, −1, 0, 1, 2, and 3. The endpoints −4 and 4 are excluded because the inequality is strict. Thus A contains exactly the seven integers listed in option A, so that set is equal to A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
