\begin{frame}{Basic Properties of Context-Free Languages} \begin{block}{Theorem} If $L_1$ is \alert{context-free} and $L_2$ \alert{regular}, then $L_1 \backslash L_2$ is \alert{context-free}. \end{block} \pause\medskip \begin{proof} $\overline{L_2}$ is regular, thus $L_1 \backslash L_2 = L_1 \cap \overline{L_2}$ is context-free. \end{proof} \pause\bigskip \begin{alertblock}{} $L_2 \backslash L_1$ is \emph{not} always context-free. Namely \begin{talign} \overline{L_1}=\Sigma^*\backslash L_1 \end{talign} \end{alertblock} \end{frame}