Title says it all.
To give a concrete example:
Let $X$ and $Y$ be non-empty sets and $f: X \rightarrow Y$ a mapping. Prove that for relation defined by $\{(x_1,x_2) \in X^2 : f(x_1) =f(x_2)\}$ reflexivity holds.
I'm not sure if it is enough to simply state that by definition every $x$ has only one image $f(x) \rightarrow f(x)=f(x)$, which is our original definition.
Appart from probably different eqvivalence classes, does it make any difference when the mapping is f.i. injective or constant ($\exists c \in Y (\forall x \in X: f(x)=c)$)?