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\documentclass{math215}

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% 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 2}
\docauthor{Your name here.}
\docdate{February 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}{1.16}  If $m$ and $n$ are even integers, then so
  is $m+n$.
\end{proposition}
\begin{pf}
Your proof goes here.  For this one, please try to use the technique 
that I introduced in class of reminding the reader of the definition
of divisibility early in the proof.  ``To show that $m+n$ is even we must show that $\ldots$''.
\end{pf}

\begin{proposition}{1.17(ii) (Our version)} If $m$ is an integer
  and $m$ is divisible by $0$, then $m=0$.
\end{proposition}
\begin{pf}
Your proof goes here.
\end{pf}

\begin{proposition}{1.18}
Let $x\in\Ints$.  If $x$ has the property that for all $m\in\Ints$,
$mx=m$, then $x=1$.
\end{proposition}
\begin{pf}
Your proof goes here.
\end{pf}

\begin{proposition}{1.19}
Let $x\in\Ints$.  If $x$ has the property that for some nonzero $m\in\Ints$,
$mx=m$, then $x=1$.
\end{proposition}
\begin{pf}
Your proof goes here.
\end{pf}

\begin{proposition}{1.24} Let $x\in\Ints$.  If $x\cdot x= x$ then $x=0$ or $x=1$.
\end{proposition}
\begin{pf}
Your proof goes here.
\end{pf}

\begin{proposition}{1.25(i)} For all $m,n\in\Ints$
\[
-(m+n) = (-m) + (-n).
\]
\end{proposition}
\begin{pf}
Your proof goes here.
\end{pf}

\begin{proposition}{1.25(ii)} For all $m\in\Ints$
\[
-m = (-1)\cdot m.
\]
\end{proposition}
\begin{pf}
Your proof goes here.
\end{pf}


\begin{proposition}{1.27(iii)} For all $m,n,p,q\in\Ints$
\[
(m-n)\cdot(p-q) = (mp + nq) -(mq+np).
\]
\end{proposition}
\begin{pf}
Your proof goes here.
\end{pf}

\begin{proposition}{1.27(v)} For all $m,n,p\in\Ints$
\[
(m-n)\cdot p = mp - np.
\]
\end{proposition}
\begin{pf}
Your proof goes here.
\end{pf}

\end{document}