If A = {x ∈ Z : −5 ≤ x < 2 and x is even}, what is A?
Answer and explanation
Correct answer: A = {−4, −2, 0}
First list the integers satisfying −5 ≤ x < 2: they are −5, −4, −3, −2, −1, 0, and 1. Now select the even integers from this list. The even numbers are −4, −2, and 0; negative integers can also be even because divisibility by 2 is what matters. The endpoints −5 and 2 are not included as even members: −5 is odd and 2 is outside the strict upper bound. Hence A = {−4, −2, 0}.
Frequently asked questions
What is the correct answer to this question?
A = {−4, −2, 0}
Why is this the correct answer?
First list the integers satisfying −5 ≤ x < 2: they are −5, −4, −3, −2, −1, 0, and 1. Now select the even integers from this list. The even numbers are −4, −2, and 0; negative integers can also be even because divisibility by 2 is what matters. The endpoints −5 and 2 are not included as even members: −5 is odd and 2 is outside the strict upper bound. Hence A = {−4, −2, 0}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
