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\newtheorem{prop}{Proposition}
\newtheorem{thm}{Theorem}
\newtheorem{lem}{Lemma}
\newtheorem{conj}{Conjecture}
\newtheorem{cor}{Corollary}
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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 sets $A$, $B$, and $C$, and functions $f:A\rightarrow B$ and
  $g:B\rightarrow C$, prove or disprove each of the following
  statements:}
\begin{enumerate}
\item \emph{If $g\circ f$ is injective, then $f$ is injective.}


\item \emph{If $g\circ f$ is injective, then $g$ is injective.}


\item \emph{If $g\circ f$ is surjective, then $f$ is surjective.}


\item \emph{If $g\circ f$ is surjective, then $g$ is surjective.}


\end{enumerate}
\end{document}
