To determine which of the given numbers are in set [tex]\(A\)[/tex], let's first describe set [tex]\(A\)[/tex]. According to the given condition, [tex]\(A\)[/tex] contains positive, odd integers less than 7.
We start by listing all the positive integers less than 7: [tex]\(1, 2, 3, 4, 5, 6\)[/tex].
Next, we identify the odd integers from this list: [tex]\(1, 3, 5\)[/tex].
Therefore, the set [tex]\(A\)[/tex] is:
[tex]\[ A = \{1, 3, 5\} \][/tex]
Now, let's check each of the given numbers to see if they are in set [tex]\(A\)[/tex]:
1. [tex]\(-1\)[/tex] is not a positive number, so it is not in set [tex]\(A\)[/tex].
2. 0 is not a positive number, so it is not in set [tex]\(A\)[/tex].
3. 1 is a positive, odd integer less than 7, so it is in set [tex]\(A\)[/tex].
4. 2 is a positive integer less than 7, but it is not odd; therefore, it is not in set [tex]\(A\)[/tex].
5. 5 is a positive, odd integer less than 7, so it is in set [tex]\(A\)[/tex].
6. 3 is a positive, odd integer less than 7, so it is in set [tex]\(A\)[/tex].
Given this analysis, we conclude that the numbers from the list that are in set [tex]\(A\)[/tex] are:
[tex]\[ 1, 5, \text{ and } 3 \][/tex]
Thus, the numbers in set [tex]\(A\)[/tex] are [tex]\(1, 5, 3\)[/tex], and these numbers are in the set [tex]\(A\)[/tex]. The numbers [tex]\(-1, 0,\)[/tex] and [tex]\(2\)[/tex] are not in the set [tex]\(A\)[/tex].
