If A = {x ∈ ℤ : x is even and −5 < x < 5}, what is A?
Answer and explanation
Correct answer: A = {−4, −2, 0, 2, 4}
The condition −5 < x < 5 allows the integers −4, −3, −2, −1, 0, 1, 2, 3, and 4. From these, the even integers are −4, −2, 0, 2, and 4. The endpoints −5 and 5 are excluded because the inequalities are strict. Zero is even because it is divisible by 2, so it must be included. Therefore, in roster form, A = {−4, −2, 0, 2, 4}.
Frequently asked questions
What is the correct answer to this question?
A = {−4, −2, 0, 2, 4}
Why is this the correct answer?
The condition −5 < x < 5 allows the integers −4, −3, −2, −1, 0, 1, 2, 3, and 4. From these, the even integers are −4, −2, 0, 2, and 4. The endpoints −5 and 5 are excluded because the inequalities are strict. Zero is even because it is divisible by 2, so it must be included. Therefore, in roster form, A = {−4, −2, 0, 2, 4}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
