If $R$ is reflexive, prove that $R^c$ is irreflexive.
If $R$ is asymmetric, prove that $R^c$ is reflexive.
Where $R^c$ = complement of $R$.
I just can't figure out anything to say for the first one because it looks like proof by definition. If $R$ is reflexive, then $R^c$ is obviously irreflexive because $aRa$ is already in $R$ and thus can't ever be in $R^c$.
I have no idea how to do the second one, because asymmetric deals with distinct elements, which doesn't seem to have any bearing on an elements relation with itself.
Any help would be appreciated, thanks!
EDIT: Solved the first one, still need help with the second.
For the second one, if $R$ is asymmetric, then $aRa\ \Rightarrow\ \neg aRa$, so that $aRa$ does not hold for any $a$. This implies that $aR^ca$ for all $a$, so that $R^c$ is reflexive.