Question

Which of the following sets, given by the roster method, is equal to the set below given in set-builder notation? x ∈ℤ

A. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
C. {0, 1, 2, ..., 99, 100}
D. {1, 2, ..., 99, 100}

Answer 1

The set 0 < x² ≤ 100 is equivalent to the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, which represents all positive integers whose squares are less than or equal to 100.

Step-by-step explanation:

We are looking for a set of integers (ℤ) that satisfies the condition 0 < x² ≤ 100. To identify this, we take the square root of 100, which gives us 10, and consider all integers whose squares fall within the range of 1 to 100 inclusively. Thus, we consider the numbers 1 through 10 as well as their negative counterparts. But since the set specifies positive integers, we eliminate the negative ones. Consequently, the correct set in roster method, which includes all positive integers whose squares are less than or equal to 100, would be {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, which is option B.