Which is the roster form of F = {x ∈ ℤ : −4 < x < 4 and x ≠ 0}?
Answer and explanation
Correct answer: F = {−3, −2, −1, 1, 2, 3}
The strict inequality −4 < x < 4 permits the integers −3, −2, −1, 0, 1, 2, and 3; the endpoints −4 and 4 are excluded. The additional condition x ≠ 0 removes 0 from this list. Therefore, F = {−3, −2, −1, 1, 2, 3}. Option C incorrectly retains zero, while option B incorrectly includes the endpoints.
Frequently asked questions
What is the correct answer to this question?
F = {−3, −2, −1, 1, 2, 3}
Why is this the correct answer?
The strict inequality −4 < x < 4 permits the integers −3, −2, −1, 0, 1, 2, and 3; the endpoints −4 and 4 are excluded. The additional condition x ≠ 0 removes 0 from this list. Therefore, F = {−3, −2, −1, 1, 2, 3}. Option C incorrectly retains zero, while option B incorrectly includes the endpoints.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
