Which roster form is correct for K = {x : x ∈ ℤ, -2 < x ≤ 3}?
Answer and explanation
Correct answer: K = {-1, 0, 1, 2, 3}
Because x is an integer and must satisfy −2 < x, the value −2 is excluded. The condition x ≤ 3 includes 3. The integers strictly greater than −2 and less than or equal to 3 are therefore −1, 0, 1, 2, and 3. Writing these elements in roster form gives K = {−1, 0, 1, 2, 3}, so option A is correct. The distractors mishandle one or both endpoints.
Frequently asked questions
What is the correct answer to this question?
K = {-1, 0, 1, 2, 3}
Why is this the correct answer?
Because x is an integer and must satisfy −2 < x, the value −2 is excluded. The condition x ≤ 3 includes 3. The integers strictly greater than −2 and less than or equal to 3 are therefore −1, 0, 1, 2, and 3. Writing these elements in roster form gives K = {−1, 0, 1, 2, 3}, so option A is correct. The distractors mishandle one or both endpoints.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
