\problemdata
{s01-ps7}
{counting relations}

\begin{problem}
On a set of $n$ elements how many of the following are there?

\begin{problemparts}

\problempart binary relations

\problempart symmetric binary relations

\problempart reflexive binary relations

\problempart symmetric and reflexive binary relations

\problempart symmetric or reflexive binary relations

\end{problemparts}
\end{problem}