![IMT Test Flight](https://writelatex.s3.amazonaws.com/published_ver/5926.jpeg?X-Amz-Expires=14400&X-Amz-Date=20240630T143324Z&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAWJBOALPNFPV7PVH5/20240630/us-east-1/s3/aws4_request&X-Amz-SignedHeaders=host&X-Amz-Signature=3496d97c33a1e728117f6935a13c06856921ad3818f06d2625d2138ac89d85bc)
IMT Test Flight
Författare
Rafael Díaz de Leon
Last Updated
för 7 år sedan
Licens
Creative Commons CC BY 4.0
Sammanfattning
Proof 1
![IMT Test Flight](https://writelatex.s3.amazonaws.com/published_ver/5926.jpeg?X-Amz-Expires=14400&X-Amz-Date=20240630T143324Z&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAWJBOALPNFPV7PVH5/20240630/us-east-1/s3/aws4_request&X-Amz-SignedHeaders=host&X-Amz-Signature=3496d97c33a1e728117f6935a13c06856921ad3818f06d2625d2138ac89d85bc)
\documentclass[letter]{article}
%% Language and font encodings
\usepackage[english]{babel}
\usepackage[utf8x]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{enumitem}
\usepackage{fancyhdr}
\pagestyle{fancy}
%% Useful packages
\usepackage{amsmath}
\usepackage{graphicx}
\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}