\documentclass[12pt, letterpaper]{amsart}

\usepackage{amsmath, amssymb, amsthm}
\usepackage[margin=.5in]{geometry}
\usepackage[pdflang={en-US}]{hyperref}

\theoremstyle{definition}
\newtheorem{dfn}{Definition}
\newtheorem{problem}{}
\newtheorem*{instructions}{Instructions}

\title{Portfolio proofs C}
\date{\today}

\begin{document} \ 

\vspace{-.25in}

\maketitle

\vspace{-.2in} 

\begin{instructions}
Choose one of the following statements and determine if it is true or false.
Use \LaTeX\ to write your proof (or disproof) nicely.
Drop your proof (both pdf and tex) in your OneDrive folder.
\end{instructions}

\begin{problem}
There are integers $m$ and $n$ such that $m^2 + mn + n^2$ is a perfect square.
\end{problem}


\begin{problem}
Suppose $A$, $B$, and $C$ are sets. If $A \times C \subseteq  B \times C$, then $A \subseteq B$.
\end{problem}


\begin{problem}
For any sets  $A$, $B$, and $C$, $(A \cap B) \times C = (A \times C) \cap (B \times C)$.
\end{problem}
\end{document}