Here's the question:
Prove or give a counterexample to the statement: If $R$ is a reflexive relation on $A$, then $R \circ R$ is also a reflexive relation on $A$.
I completely understand how it works from an intuitive point of view because this means $a\in A \Rightarrow (a,a)\in R$ so plugging the result of $aRa$ (which is $a$) back into $R$ will give you $a$ again. I'm just having a hard time explaining this in the form of a formal proof since $R(R(a,a))$ seems like it would only be proper notation if $R$ was a function and not just a relation and I can't find good examples of proofs involving composition of relations.