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\title{COSC-4765-HW2-TEMPLATE}
\author{Rafael Diaz de Leon Plata}
\lhead{Test Flight}
\cfoot{Introduction to Mathematical Thinking}
\begin{document}
\section{Problem}
Say whether the following is true or false and support your answer by a proof.
$$
(\exists m \in {\cal N})(\exists n \in {\cal N})(3m + 5n = 12)
$$
\subsection{Solution}
This is false, proof:
By algebra, we re-arrange the equation
$$
m = 4 - (5/3)*n
$$
The minimum value of $ n \in {\cal N} $ that would gives us an integer $m$ is 3,
but this gives us $ m = - 1 $, we can see that any greater value for $n$ would
give us a more negative value for $m$, so we can see that there is not a pair
of natural number that fulfill the given conditions. $QED$.
\end{document}
