To determine which set represents the same relation as the table given, let's consider the table pairs and compare each proposed set.
The table provided is:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
0 & 5 \\
\hline
4 & 2 \\
\hline
6 & 9 \\
\hline
9 & 10 \\
\hline
\end{array}
\][/tex]
This can be represented as the set of pairs:
[tex]\(\{ (0, 5), (4, 2), (6, 9), (9, 10) \}\)[/tex]
### Let's examine each given set:
1. Set 1: [tex]\(\{ (0, 5), (4, 2), (6, 9), (9, 10) \}\)[/tex]
This set exactly matches the table's relation:
[tex]\[
\{ (0, 5), (4, 2), (6, 9), (9, 10) \}
\][/tex]
So this set represents the same relation as the table.
2. Set 2: [tex]\(\{ (5, 0), (2, 4), (3, 0), (10, 5) \}\)[/tex]
- (5, 0): not in the table
- (2, 4): not in the table
- (3, 0): not in the table
- (10, 5): not in the table
This set does not represent the same relation as the table.
3. Set 3: [tex]\(\{ 0, 2, 4, 5, 6, 9, 10 \}\)[/tex]
This set contains individual elements rather than pairs. Therefore, it doesn't represent a relation.
4. Set 4: [tex]\(\{ 2, 5, 3, 10 \}\)[/tex]
Similar to Set 3, this set contains individual elements, not pairs, and doesn't represent a relation.
### Conclusion:
Among the given sets, only the first set:
[tex]\(\{ (0, 5), (4, 2), (6, 9), (9, 10) \}\)[/tex]
accurately represents the same relation as the table. Therefore, the correct answer is Set 1.
