Equivalence relations 
Having trouble proving this is an equivalence relation.
Is it suffice to say that let $x y z$ be any string in $\Sigma^*$, 
$(xz \in L \iff yz \in L) \rightarrow (yz \in L \iff xz \in L)$ shows that $xRy \rightarrow yRx$?

For any $x\in \Sigma^*$, define $L(x)$ to be the language $\{z\in \Sigma^*\mid xz\in L\}$.  Then the definition of $R$ can be rephrased as
$$xRy \iff L(x)=L(y).$$
This is clearly reflexive, symmetric, and transitive, but assuming this is an elementary course you probably want to at least write out transitivity, making clear you understand why $xRy$ and $yRz$ imply $xRz$.
