If R₁ = {x : x ∈ ℤ, x² ≤ 9 and x is odd}, what is R₁?
Answer and explanation
Correct answer: R₁ = {-3, -1, 1, 3}
The governing concept is combining an inequality with an integer and parity condition. From x² ≤ 9, we get |x| ≤ 3, so the possible integers are −3, −2, −1, 0, 1, 2, and 3. Filtering these for odd values leaves −3, −1, 1, and 3. Therefore R₁ = {-3, -1, 1, 3}, making option A correct. B includes even integers, C omits valid endpoints, and D incorrectly includes zero.
Frequently asked questions
What is the correct answer to this question?
R₁ = {-3, -1, 1, 3}
Why is this the correct answer?
The governing concept is combining an inequality with an integer and parity condition. From x² ≤ 9, we get |x| ≤ 3, so the possible integers are −3, −2, −1, 0, 1, 2, and 3. Filtering these for odd values leaves −3, −1, 1, and 3. Therefore R₁ = {-3, -1, 1, 3}, making option A correct. B includes even integers, C omits valid endpoints, and D incorrectly includes zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
