\begin{frame}{Operations on Languages}
  \begin{block}{Set operations}
    A language is a \emph{set} of words.
    \smallskip
    So the usual set operations have meaning for languages:
    \centerline{$\in$,\; $\subseteq$,\; $\cap$,\; $\cup$,\; $\setminus$,\; \ldots}
  \end{block}
  \pause

  \begin{exampleblock}{}\vspace{-.5ex}
    \begin{malign}
      ba \in \{\,a,aba,ba\,\} &&
      ab \not\in \{\,a,aba,ba\,\}
    \end{malign}
  \end{exampleblock}
  \pause

  \begin{exampleblock}{}\vspace{-.5ex}
    \begin{malign}
      \{\,a,ba\,\} \subseteq \{\,a,aba,ba\,\} &&
      \{\,a,b\,\} \not\subseteq \{\,a,aba,ba\,\}
    \end{malign}
  \end{exampleblock}
  \pause
  
  \begin{exampleblock}{}\vspace{-.5ex}
    \begin{malign}
      \{\,a,aba,ba\,\} \cap \{\,a, ab, ba \,\} = \{\,a,ba\,\}
    \end{malign}
  \end{exampleblock}
  \pause

  \begin{exampleblock}{}\vspace{-.5ex}
    \begin{malign}
      \{\,a,aba,ba\,\} \cup \{\,a, ab, ba \,\} = \{\,a,ab,aba,ba\,\}
    \end{malign}
  \end{exampleblock}
  \pause

  \begin{exampleblock}{}\vspace{-.5ex}
    \begin{malign}
      \{\,a,aba,ba\,\} \setminus \{\,a, ab, ba \,\} = \{\,aba\,\}
    \end{malign}
  \end{exampleblock}
\end{frame}