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\documentclass{math215}

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% following to use Times as the default font insteand of
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\usepackage{times,txfonts}

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\doclabel{Math 215: Homework 11}
\docauthor{Your name here}
\docdate{April 13, 2012}

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% by uncommenting the line below.  Feel free to make changes to that file.
\input{math215extras.tex}

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\begin{document}
\par
\begin{proposition}{8.40}\noindent
  \begin{itemize}
    \item[(i)] Let $x\in \Reals$.  Then $x>0$ if and only if $1/x>0$.
    \item[(ii)] Let $x,y\in\Reals$ such that $0<x<y$.  Then $0<1/y<1/x$.
\end{itemize}    
\end{proposition}
\begin{proof}
\end{proof}

\begin{proposition}{8.43}  Let $x,y\in\Reals$ such that $x<y$.
  Then there exists $z\in\Reals$ such that $x<z<y$.
\end{proposition}
\begin{proof}
\end{proof}

\begin{proposition}{9.11}  If $f:A\rightarrow B$ has an inverse
  function, the inverse function is unique.
\end{proposition}
\begin{proof}
\end{proof}

\begin{project}{9.A}
\noindent
\begin{enumerate}
\item State the negation of:\\
If $A\subseteq B$ and $B$ is countable, then $A$ is either empty,
or finite, or countable.
\item State the contrapositive of:\\
If $A\subseteq B$ and $B$ is countable, then $A$ is either empty,
or finite, or countable.
\item State the negation of:\\
If $x\in \Reals$, there exists $n\in\Nats$ such that $n>x$.
\item State the converse of:\\ 
If $f\circ g$ is bijective, then $f$ is surjective and
$g$ is injective.
\item State the converse of the contrapositive of:\\ 
If $f\circ g$ is bijective, then $f$ is surjective and
$g$ is injective.
\end{enumerate}


\end{project}

\end{document}