\documentclass[12pt]{article}

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\usepackage{fancyhdr,lastpage}
\usepackage{amsmath,amsthm,amssymb}
\usepackage{tikz}
\usepackage{multirow}
\usepackage{substr}
\usepackage{pgfplots}

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% This redefines "\neg" -- the logical negation -- to be a tilde
% rather than an angular negation sign.
\renewcommand*{\neg}{\mathord{\sim}}

% Include "solution" in your filename to make sure the right mode is
% used below.

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  % Solutions
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}
{%
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\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--02}
\chead{Problem of the Day\answer{ solution}}
\rhead{}
\lfoot{}
\cfoot{\answer{Page \thepage\ of \pageref{LastPage}}}
\rfoot{due Tuesday, December 2, 2014}

\begin{document}
\question{Formally prove the following statements about the cardinalities
  of (not necessarily finite) sets --- do not appeal to intuition!}

\begin{itemize}
\item \question{If $A\subseteq B\subseteq C$ and $|A|\geq|C|$, then
    $|A|=|B|$.}
  
  \answer{}
  
\item \question{If $|A|\leq |B|$, then $|\mathcal P(A)|\leq|\mathcal
    P(B)|$.}
  
  \answer{}

\end{itemize}

\end{document}