Which is the correct roster form for H = {x ∈ ℤ : −2 < x ≤ 3}?
Answer and explanation
Correct answer: H = {−1, 0, 1, 2, 3}
The inequality has two different boundary conditions. The sign −2 < x means that −2 is excluded, while x ≤ 3 means that 3 is included. The integers strictly greater than −2 and less than or equal to 3 are −1, 0, 1, 2, and 3. Consequently, H = {−1, 0, 1, 2, 3}, so option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
H = {−1, 0, 1, 2, 3}
Why is this the correct answer?
The inequality has two different boundary conditions. The sign −2 < x means that −2 is excluded, while x ≤ 3 means that 3 is included. The integers strictly greater than −2 and less than or equal to 3 are −1, 0, 1, 2, and 3. Consequently, H = {−1, 0, 1, 2, 3}, so option A is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
