What is the roster form of F = {x : x = 2n + 1, n ∈ ℤ, −2 ≤ n ≤ 2}?
Answer and explanation
Correct answer: F = {-3, -1, 1, 3, 5}
The governing concept is converting a bounded parameterized set into roster form. The integers satisfying −2 ≤ n ≤ 2 are −2, −1, 0, 1, and 2. Substitution into x = 2n + 1 gives −3, −1, 1, 3, and 5 respectively. Since a set lists each distinct value once, F = {-3, -1, 1, 3, 5}. Therefore option A is correct. Option B starts with the value obtained from n = −3, which is outside the stated range.
Frequently asked questions
What is the correct answer to this question?
F = {-3, -1, 1, 3, 5}
Why is this the correct answer?
The governing concept is converting a bounded parameterized set into roster form. The integers satisfying −2 ≤ n ≤ 2 are −2, −1, 0, 1, and 2. Substitution into x = 2n + 1 gives −3, −1, 1, 3, and 5 respectively. Since a set lists each distinct value once, F = {-3, -1, 1, 3, 5}. Therefore option A is correct. Option B starts with the value obtained from n = −3, which is outside the stated range.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
