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\begin{center}\textbf{Problem Set 1 \hspace{.7in} Foundations \hspace{.7in} Due 1/16/17} \end{center}

\noindent Four of these problems will be graded (our choice, not yours!), with each problem worth 5 points.  Clear and complete justification is required for full credit.  You are welcome to discuss these problems with anyone and everyone, but must write up your own final submission without reference to any sources other than the textbook and instructor. 

\begin{enumerate}
\item The sum of an odd and an odd integer is even.

\item If $p, q, r \in \mathbb{Z}$ with $p,q,$ and $r$ odd, then $p+q+r$ is odd.

\item If $p, q, r \in \mathbb{Z}$ with $p+q+r$ odd, then $p, q,$ and $r$ are odd.

\item The product of an even and an odd integer is even.

\item The sum of a throddodd and a throddodd integer is throdd.

\item The product of a throdd and a throdd integer is throdd.

\item The cube of a throddodd is throddodd.

\item The sum of any three consecutive integers is threven

\end{enumerate}

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