If $R,S$ are reflexive relations, so are $R \oplus S$ and $R \setminus S$? 
Suppose $R$ and $S$ are reflexive relations on a set $A$. Prove or disprove each of these statements.
a) $R\oplus S$ is reflexive.
b) $R\setminus S$ is reflexive.

I think both of a) and b) are false, but I'm having trouble with coming up with counterexamples.

Assuming $A \neq \emptyset$ consider $R=S= \{ (a,a) : a \in A \}$.
