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\newtheorem{thm}{Theorem}
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\lhead{MATH 311-01}
\chead{Problem of the Day}
\rhead{YOUR NAME HERE}
\lfoot{}
\cfoot{Page \thepage\ of \pageref{LastPage}}
\rfoot{\textbf{due November 8, 2013}}
\begin{document}
\emph{For a set $A$ and $B$ a proper subset of $A$, let $f$ be a
  function from $A$ to $B$. $f$ is a subset of $A\times B$, and thus a
  subset of $A\times A$. We may thus consider $f$ as a \emph{relation}
  on $A$, and investigate its properties:}
% Hint: Since $B\subsetneq A$, there is at least one element of $A$
% which is not an element of $B$; looking at how $f$ relates to this
% element is illuminating.
\begin{enumerate}
\item \emph{Prove that, considered as a relation on $A$, $f$ is
    \emph{not} reflexive.}

  \begin{proof}
    
  \end{proof}

\item \emph{Prove that, considered as a relation on $A$, $f$ is
    \emph{not} symmetric.}

  \begin{proof}
    
  \end{proof}

\item \emph{Give an example of two different functions (on different
    $A$ and $B$, if you wish) which, when considered as relations on
    $A$, demonstrate both transitivity and non-transitivity.}



\end{enumerate}
\end{document}
