What is the correct roster form of W = {x : x ∈ ℤ, x² < 2}?
Answer and explanation
Correct answer: W = {-1, 0, 1}
Since x is restricted to integers, inspect the integers near zero. The values −1, 0, and 1 have squares 1, 0, and 1, all of which are less than 2. The next integers, −2 and 2, have square 4 and therefore fail the strict inequality. All integers farther from zero have even larger squares. Thus the complete roster form is {−1, 0, 1}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
W = {-1, 0, 1}
Why is this the correct answer?
Since x is restricted to integers, inspect the integers near zero. The values −1, 0, and 1 have squares 1, 0, and 1, all of which are less than 2. The next integers, −2 and 2, have square 4 and therefore fail the strict inequality. All integers farther from zero have even larger squares. Thus the complete roster form is {−1, 0, 1}, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
