# Set theory - Relations, equivalence relations

If $X = \{1,2,3\}$ then a partition of $C$ of $X$ could be $\{\{1\},\{2,3\}\}$. Correct?

Does this partition equal the relation $\{(1,1),(2,3),(2,2),(3,3),(3,2)\}$ is this an equivalence relation? Does the set of equivalence classes $= \{\{1\},\{2,3\}\}$?

Sorry I just trying to understand the relationship between equivalence relations and partitions.

Partitions and equivalence relations on a set $X$ determine each other, but they are not equal.