To determine which table accurately represents the same relation as the set [tex]\(\{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\)[/tex], we need to check each table one by one.
### Given Relation:
The given set of pairs is:
[tex]\[ \{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\} \][/tex]
### Table 1:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-6 & -3 \\
\hline
4 & 2 \\
\hline
-4 & -1 \\
\hline
0 & 2 \\
\hline
\end{array}
\][/tex]
The pairs in Table 1 are:
[tex]\[ \{(-6, -3), (4, 2), (-4, -1), (0, 2)\} \][/tex]
Comparing these pairs to the given set:
- [tex]\((-6, -3) \neq (-6, 4)\)[/tex]
- [tex]\((4, 2) \neq (-4, 0) \text{ or any other pair in the given set}\)[/tex]
- [tex]\((-4, -1) \neq (-4, 0)\)[/tex]
- [tex]\((0, 2) \neq (-1, 2) \text{ or any other pair in the given set}\)[/tex]
We see that none of the pairs match, so Table 1 does not represent the given relation.
### Table 2:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-6 & 4 \\
\hline
-4 & 0 \\
\hline
-3 & 2 \\
\hline
-1 & 2 \\
\hline
\end{array}
\][/tex]
The pairs in Table 2 are:
[tex]\[ \{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\} \][/tex]
Comparing these pairs to the given set:
- [tex]\((-6, 4) = (-6, 4)\)[/tex]
- [tex]\((-4, 0) = (-4, 0)\)[/tex]
- [tex]\((-3, 2) = (-3, 2)\)[/tex]
- [tex]\((-1, 2) = (-1, 2)\)[/tex]
Each pair matches exactly, so Table 2 represents the given relation.
### Table 3:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
6 & 4 \\
\hline
4 & 0 \\
\hline
3 & 2 \\
\hline
1 & 2 \\
\hline
\end{array}
\][/tex]
The pairs in Table 3 are:
[tex]\[ \{(6, 4), (4, 0), (3, 2), (1, 2)\} \][/tex]
Comparing these pairs to the given set:
- [tex]\((6, 4) \neq (-6, 4)\)[/tex]
- [tex]\((4, 0) \neq (-4, 0)\)[/tex]
- [tex]\((3, 2) \neq (-3, 2)\)[/tex]
- [tex]\((1, 2) \neq (-1, 2)\)[/tex]
None of the pairs match, so Table 3 does not represent the given relation.
### Conclusion:
Only Table 2 correctly represents the same relation as the set [tex]\(\{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\)[/tex].
