\documentclass[12pt]{article}

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\usepackage{amsmath,amsfonts,amssymb,amsthm}
\newtheorem{prop}{Proposition}
\newtheorem{thm}{Theorem}
\newtheorem{lem}{Lemma}
\newtheorem{conj}{Conjecture}
\newtheorem{cor}{Corollary}
\theoremstyle{definition}
\newtheorem{defn}{Definition}

\pagestyle{fancy}

\lhead{MATH 311-01}
\chead{Problem of the Day}
\rhead{YOUR NAME HERE}
\lfoot{}
\cfoot{Page \thepage\ of \pageref{LastPage}}
\rfoot{\textbf{due December 4, 2013}}
\begin{document}
\begin{enumerate}
\item \emph{Prove that there are infinitely many prime numbers
    congruent to 5 modulo 6.}

  \begin{proof}
    
  \end{proof}

\item
  \begin{enumerate}
  \item \emph{Prove that for any sets $A$ and $B$, $\mathcal P(A\cap
      B)=\mathcal P(A)\cap\mathcal P(B)$.}

    \begin{proof}
      
    \end{proof}

  \item \emph{Prove that for sets $A$ and $B$, $\mathcal P(A\cap
      B)=\mathcal P(A)\cap\mathcal P(B)$ if and only if $A\subseteq B$
      or $B\subseteq A$.}

    \begin{proof}
      
    \end{proof}
  \end{enumerate}
\end{enumerate}
\end{document}
