Which is the roster form of F₁ = {x ∈ ℤ : −4 ≤ x ≤ 4 and x is odd}?
Answer and explanation
Correct answer: {−3, −1, 1, 3}
The inclusive interval −4 ≤ x ≤ 4 contains the integers −4, −3, −2, −1, 0, 1, 2, 3, and 4. Selecting only the odd integers removes −4, −2, 0, 2, and 4, leaving −3, −1, 1, and 3. The endpoints −4 and 4 are included in the interval, but they are even and therefore do not belong to the set. Hence the roster form is {−3, −1, 1, 3}, option A.
Frequently asked questions
What is the correct answer to this question?
{−3, −1, 1, 3}
Why is this the correct answer?
The inclusive interval −4 ≤ x ≤ 4 contains the integers −4, −3, −2, −1, 0, 1, 2, 3, and 4. Selecting only the odd integers removes −4, −2, 0, 2, and 4, leaving −3, −1, 1, and 3. The endpoints −4 and 4 are included in the interval, but they are even and therefore do not belong to the set. Hence the roster form is {−3, −1, 1, 3}, option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
