To determine which table represents the same relation as the set [tex]\(\{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\)[/tex], we need to compare each given table with this set. We essentially need to find which table(s) contain the exact same pairs, without any differences. Each given table will be considered as a list of pairs.
Here are the given tables:
1. Table 1:
[tex]\[ \{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\} \][/tex]
2. Table 2:
[tex]\[ \{(-6, 0), (-4, 4), (-1, 2), (-3, 2)\} \][/tex]
3. Table 3:
[tex]\[ \{(4, -6), (0, -4), (2, -3), (2, -1)\} \][/tex]
4. Table 4:
[tex]\[ \{(-1, -2), (-2, -3), (-4, 0), (-6, 4)\} \][/tex]
5. Table 5:
[tex]\[ \{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\} \][/tex]
Let's compare each table to the given relation set [tex]\(\{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\)[/tex]:
1. Table 1 is [tex]\(\{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\)[/tex]. It matches exactly with the given set.
2. Table 2 is [tex]\(\{(-6, 0), (-4, 4), (-1, 2), (-3, 2)\}\)[/tex]. This does not match the given set because the pairs are different.
3. Table 3 is [tex]\(\{(4, -6), (0, -4), (2, -3), (2, -1)\}\)[/tex]. This does not match the given set because the pairs are different and the order is reversed.
4. Table 4 is [tex]\(\{(-1, -2), (-2, -3), (-4, 0), (-6, 4)\}\)[/tex]. This does not match the given set because the pairs are completely different.
5. Table 5 is [tex]\(\{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\)[/tex]. It matches exactly with the given set.
Based on the comparison, we can see that Table 1 and Table 5 represent the same relation as the set [tex]\(\{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\)[/tex].
Thus, the tables that represent the same relation are:
[tex]\[ \boxed{1 \text{ and } 5} \][/tex]
