Which is the roster form of D₂ = {x ∈ ℤ : x is even and −5 < x < 5}?
Answer and explanation
Correct answer: {−4, −2, 0, 2, 4}
The condition −5 < x < 5 restricts x to the integers −4, −3, −2, −1, 0, 1, 2, 3, and 4. From these integers, the even numbers are −4, −2, 0, 2, and 4. Both endpoints −5 and 5 are excluded because the inequalities are strict. Therefore, the roster form is {−4, −2, 0, 2, 4}. Zero is included because zero is an even integer.
Frequently asked questions
What is the correct answer to this question?
{−4, −2, 0, 2, 4}
Why is this the correct answer?
The condition −5 < x < 5 restricts x to the integers −4, −3, −2, −1, 0, 1, 2, 3, and 4. From these integers, the even numbers are −4, −2, 0, 2, and 4. Both endpoints −5 and 5 are excluded because the inequalities are strict. Therefore, the roster form is {−4, −2, 0, 2, 4}. Zero is included because zero is an even integer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
