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\begin{document}

\begin{center}
{\Large{\color{blue}Quiz 1}}
\end{center}
{\bf Instructions:} 
Show your work and explain every step. 


\begin{enumerate}

\item (9 points) Express the following as a formula and find its negation and its contrapositive. Indicate which is which.

\begin{center}
If $m$ is an even integer, then there exists an integer $k$ such that $m = 2k$.
\end{center}

\vspace{2 in}

\item Prove or disprove the following (i.e. if the statement is true, prove it, and if the statement 
is false, write down a counterexample). Write down the method of proof you're using. 

\begin{enumerate}

\item (6 points) The set $\R^+$ of positive real numbers has no smallest element. 

\vspace{1.5 in}

\item (5 points) If $x$ and $y$ are irrational, then $x^y$ is irrational.

\end{enumerate}

\end{enumerate}
\end{document}