Which roster form is correct for Z = {x : x ∈ Z, −2 ≤ x < 4}?
Answer and explanation
Correct answer: Z = {-2, -1, 0, 1, 2, 3}
The governing concept is listing integers in a half-open interval. The lower condition −2 ≤ x includes −2, while the upper condition x < 4 excludes 4. The consecutive integers from −2 through 3 are −2, −1, 0, 1, 2, and 3. Hence option C is correct. Option A incorrectly includes 4, B omits the allowed endpoint −2, and D omits 0 even though zero is an integer in the interval.
Frequently asked questions
What is the correct answer to this question?
Z = {-2, -1, 0, 1, 2, 3}
Why is this the correct answer?
The governing concept is listing integers in a half-open interval. The lower condition −2 ≤ x includes −2, while the upper condition x < 4 excludes 4. The consecutive integers from −2 through 3 are −2, −1, 0, 1, 2, and 3. Hence option C is correct. Option A incorrectly includes 4, B omits the allowed endpoint −2, and D omits 0 even though zero is an integer in the interval.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
