Which is the roster form of M = {x : x ∈ ℤ and −2 ≤ x < 3}?
Answer and explanation
Correct answer: M = {−2, −1, 0, 1, 2}
The governing concept is translating interval bounds for integers into a roster. The lower inequality −2≤x is inclusive, so −2 must be listed. The upper inequality x<3 is strict, so 3 must not be listed. The integers between these bounds are −2, −1, 0, 1, and 2. Option B shifts the lower endpoint and includes 3, C omits 0, and D incorrectly includes 3. Hence A is correct.
Frequently asked questions
What is the correct answer to this question?
M = {−2, −1, 0, 1, 2}
Why is this the correct answer?
The governing concept is translating interval bounds for integers into a roster. The lower inequality −2≤x is inclusive, so −2 must be listed. The upper inequality x<3 is strict, so 3 must not be listed. The integers between these bounds are −2, −1, 0, 1, and 2. Option B shifts the lower endpoint and includes 3, C omits 0, and D incorrectly includes 3. Hence A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
