Table of definitions formatting help

Question

I'm using the following code to produce a table of definitions.

\begin{tabular}{rl}
$R$ is... & ...if and only if... \\
\hline
irreflexive & for all $x$ iht $xx \notin R$. \\
\hline
transitive & for all $xyo$ iht if $xo \in R$ and $oy \in R$, then $xy \in R$. \\
\hline
antisymmetric & for all $xy$ iht if $xy \in R$ and $yx \in R$, then $x=y$. \\
\hline
a partial order & $R$ is transitive and antisymmetric. \\
\hline
\end{tabular}`

To be honest, the final output looks pretty mediocre. Any ideas for how to improve it?

EDIT: Here's a complete file, featuring a second attempt at the table. Neither are very satisfactory, in my opinion.

\documentclass{article}
\usepackage{graphicx}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{eulervm}
\usepackage{stmaryrd}

\usepackage{tabularx}
\setlength{\extrarowheight}{2pt}

\usepackage{amsthm}
\theoremstyle{definition}
\newtheorem{defi}{Definition}

\begin{document}
\begin{defi} Fix arbitrary $R$. Then ($R$ is a \textit{relation}) if and only if ($R$ is a set, and every element of $R$ is an ordered pair). Supposing $R$ is indeed a relation, then the following hold.

\begin{center}
\begin{tabular}{|rl|}
\hline
$R$ is... & ...if and only if... \\
\hline
irreflexive & for all $x$ iht $xx \notin R$. \\
\hline
transitive & for all $xyo$ iht if $xo \in R$ and $oy \in R$, then $xy \in R$. \\
\hline
antisymmetric & for all $xy$ iht if $xy \in R$ and $yx \in R$, then $x=y$. \\
\hline
a partial order & $R$ is transitive and antisymmetric. \\
\hline
\end{tabular}\end{center}\end{defi}
\end{document}

Answer 1

As mentioned in the comments, it seems rahter subjective, but here is my take on it.

I'd say use less lines and if so use different lines, for example using the booktabs package with \toprule, \midrule and \bottomrule. Also you can introduce a definitionsymbol; as notation is somewhat unregular use whatever is familiar to you. In the following I'll use :\Leftrightarrow .

Code

\documentclass{article}
\usepackage{booktabs}
\begin{document}

\begin{tabular}{l c p{.5\textwidth}}
\toprule
$R$ is...       &                  & ...if and only if... \\
\midrule
irreflexive     &$:\Leftrightarrow$& for all $x$ iht $xx \notin R$. \\
transitive      &$:\Leftrightarrow$& for all $xyo$ iht if $xo \in R$ and $oy \in R$, then $xy \in R$. \\
antisymmetric   &$:\Leftrightarrow$& for all $xy$ iht if $xy \in R$ and $yx \in R$, then $x=y$. \\
a partial order &$:\Leftrightarrow$& $R$ is transitive and antisymmetric. \\
\bottomrule
\end{tabular}

\end{document}

Result