To solve the problem of determining which set represents the same relation as the table provided, we need to critically examine each set to see if it matches the given relation in the table. The table of relations is as follows:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $f(x)$ \\
\hline
0 & 5 \\
\hline
4 & 2 \\
\hline
6 & 9 \\
\hline
9 & 10 \\
\hline
\end{tabular}
\][/tex]
This table shows that the relation is a set of ordered pairs: [tex]\(\{(0, 5), (4, 2), (6, 9), (9, 10)\}\)[/tex].
Let's analyze each provided set:
1. Set 1: [tex]\(\{(5,0),(2,4),(3,6),(10,9)\}\)[/tex]
- This set contains the pairs: [tex]\((5, 0), (2, 4), (3, 6), (10, 9)\)[/tex].
- Comparing this to our table, none of these pairs match the original pairs.
2. Set 2: [tex]\(\{0,2,4,5,6,9,10\}\)[/tex]
- This set contains the individual elements: [tex]\(0, 2, 4, 5, 6, 9, 10\)[/tex].
- These are simply elements, not ordered pairs, so this set does not represent the relation as ordered pairs are required.
3. Set 3: [tex]\(\{2,5,9,10\}\)[/tex]
- This set contains the elements: [tex]\(2, 5, 9, 10\)[/tex].
- Similar to Set 2, these are just individual elements and do not form pairs representing the relation.
Comparing these sets to the given relation:
- None of the sets exactly matches the original pairs [tex]\(\{(0, 5), (4, 2), (6, 9), (9, 10)\}\)[/tex].
Therefore, the correct answer is [tex]\(0\)[/tex], implying that none of the sets provided represent the same relation as the table shown.
