I have two relations:
$$\begin{align} A &= \{(x,y), (y,z), (z,x)\} \\ B &= \{(y,x), (z,y), (x,z)\} \end{align}$$
Both on $\{x,y,z\}$.
I know neither relation is an equivalence relation as they don't exhibit reflexivity, transitivity, or symmetry. $A \cup B$ shows transitivity and reflexivity, but not symmetry.
I want to find $A \circ B$: what does this look like, and what are its equivalence classes? I'm not familiar with this symbol but I am with cross product ($\times$), is it related?