
Getting the line that splits down the variables column is giving me trouble.
You should not try to split the colums rather than merging the headline cell:
\begin{table}
\centering
\begin{tabular}{|c|c|c|c|c|c|}
\toprule
\multicolumn{2}{c}{Variables} & Statement & Inverse & Converse & Contrapositive\\
\midrule
\textit{p} & \textit{q} & & & \\
\bottomrule
\end{tabular}
\end{table}
\multicolumn, see e.g. How to merge columns in a table? – Torbjørn T. Nov 21 '14 at 23:58