%%% Preamble starts here.
\documentclass{math215}

% Include any special packages you might use.  Uncomment the
% following to use Times as the default font insteand of
% TeX's default font of Computer Modern.
\usepackage{times,txfonts}

% The following commands set up the material that appears
% in the header.
\doclabel{Math 215: Homework 6}
\docauthor{Your name here}
\docdate{March 2, 2012}

% I've provided a file (math215extras.tex) with some commonly used extra 
% commands. If you've downloaded it, you can include it in your document
% by uncommenting the line below.  Feel free to make changes to that file.
\input{math215extras.tex}

%%%% Main document starts here.

\begin{document}

\begin{proposition}{5.4}
  Let $A$, $B$, $C$ be sets.  
\begin{itemize}
  \item[(i)] $A=A$.
  \item[(ii)] If $A=B$ then $B=A$.
  \item[(iii)] If $A=B$ and $B=C$ then $A=C$.
\end{itemize}
\end{proposition}
\begin{proof}
  Your proof goes here.
\end{proof}

\begin{project}{5.12 (partial)}
For each of the following double implications $P\iff Q$ determine which 
of the implications $P\implies Q$ or $Q\implies P$, if any, are true.
For the ones that are true, prove them.  For the ones are are not
true, provide a counterexample.
\item[(ii)] $C\subseteq A$ or $C\subseteq B$ $\iff$ $C\subseteq(A\cup B)$
\item[(iii)] $C\subseteq A$ and $C\subseteq B$ $\iff$ $C\subseteq(A\cap B)$
\end{project}

% 
% \begin{proposition}{5.14}  Let $A,B\subseteq X$.  Then $A\subseteq B$ if and only if $B^c\subseteq A^c$.
% \end{proposition}
% \begin{proof}
% Your proof goes here.
% \end{proof}

\end{document}
