What is the set $[4]$
but I haven't seen any examples in the text that describe how to approach a question such as this one.
$R=\{(1,1),(2,2),(1,2),(2,1),(1,3),(3,1),(3,2),(2,3),(3,3),(4,4),(5,5),(4,5),(5,4)\}$
I can see that the relation is symmetric, transitive, and reflexive, but not sure how I can use this information for solving the problem.
Any hints that you can provide are appreciated (not looking for a solution).
Clarification
Notation $[4]$ means the equivalence class of the element $4$.
The set $[4]$ is the equivalence class of $4$ in an equivalence relation $R$. It is the set of all elements that are related (or "equivalent") to $4$. To figure this out, just scan the ordered pairs of $R$ and look for the ones that contain a $4$ (or, by the transitivity of $R$, any other element in $[4]$; note that by the reflexivity of $R$, we know that $4 \in [4]$), then add the other element to the set. For example, in this case we have: $$ [1] = [2] = [3] = \{1,2,3\} $$