[Tex/LaTex] Two enumerated lists side by side

Question

I am trying to replicate the image below, but what I currently have gives awkward spacing on the two lists. Could anyone advise me as to how I could mimic the picture?

\documentclass[12pt,letterpaper]{article}

\usepackage{enumerate,multicol}
\usepackage{amsmath, amssymb, amsthm}

\begin{document}

\begin{multicols}{2}
\textbf{\emph{Possible Structural Properties}}
\begin{enumerate}[1.]
\item The set has 4 elements.
\item The operation is commutative.
\item $x \ast x = x$ for all $x \in S$
\item The equation $a \ast x = b$ has a solution $x$ in $S$ for all $a,b \in S$.
\end{enumerate}
\textbf{\emph{Possible Nonstructural Properties}}
\begin{enumerate}[a.]
\item The number 4 is an element.
\item The operation is called ``addition.''
\item The elements of $S$ are matrices.
\item $S$ is a subset of $\mathbb{C}$.
\end{enumerate}
\end{multicols}

\end{document}

Answer 1

I chose to do it with two \parboxes and the enumitem package.

\documentclass{article}
\usepackage{amssymb}
\usepackage{enumitem}
\begin{document}
\noindent\parbox[t]{2.4in}{\raggedright%
\textbf{\textit{Possible Structural Properties}}
\begin{enumerate}[topsep=0pt,itemsep=-2pt,leftmargin=13pt]
\item The set has 4 elements.
\item The operation is commutative.
\item $x \ast x = x$ for all $x \in S$
\item The equation $a \ast x = b$ has a solution $x$ in $S$ for all $a,b \in S$.
\end{enumerate}
}%
\parbox[t]{2.4in}{\raggedright%
\textbf{\textit{Possible Nonstructural Properties}}
\begin{enumerate}[topsep=0pt,itemsep=-2pt,leftmargin=13pt]
\item[a.] The number 4 is an element.
\item[b.] The operation is called ``addition.''
\item[c.] The elements of $S$ are matrices.
\item[d.] $S$ is a subset of $\mathbb{C}$.
\end{enumerate}
}
\end{document}