\begin{frame}
\frametitle{Exercises}
\begin{minipage}{0.49\textwidth}
\begin{center}
\begin{tikzpicture}[
default,
point/.style={circle, draw=blue, thick, inner sep=3pt, minimum size=9mm},
node distance=20mm]
\node (1) [point] {\lab{p}};
\node [alo=1] {$w_1$};
\node (2) [point, below left of=1] {\lab{q}};
\node [alo=2] {$w_2$};
\node (3) [point, below right of =1] {\lab{p,\;r}};
\node [aro=3] {$w_3$};
\begin{scope}[shorten <= 1mm, shorten >= 1mm, very thick,>=stealth]
\draw [->] (1) to[bend left=15] (2);
\draw [->,red] (2) to[bend left=15] (1);
\draw [->] (1) to (3);
\draw [->] (3) to (2);
\end{scope}
\draw [rounded corners=2mm, dashed] (-25mm,-20mm) rectangle (25mm,8mm);
\end{tikzpicture}
\vspace{1ex}
\end{center}
\end{minipage}
\begin{minipage}{0.50\textwidth}
\begin{itemize}
\item $\BLUE{W}= \{w_1,w_2,w_3\}$
\item $R = \{\langle w_1,w_2\rangle ,\langle w_1,w_3\rangle, $ \\
\;\hfill $ \langle w_2,w_1\rangle , \langle w_3,w_2\rangle \}$
\item $\lab{L}(w_1) = \{\lab{p}\}$ \\
$\lab{L}(w_2) =\{ \lab{q}\}$ \\
$\lab{L}(w_3) =\{ \lab{p,r}\}$
\end{itemize}
\end{minipage}
\medskip
\begin{exampleblock}{Check for yourself:}
\begin{malign}
w_2 &\;\models\; \all r \wedge \all p & \mbox{\DARKRED{?}}\\
w_1 &\;\models\; \all p & \mbox{\DARKRED{?}}\\
w_1 &\;\models\; \some \all p & \mbox{\DARKRED{?}}\\
w_1 &\;\models\; \all \some p & \mbox{\DARKRED{?}}
\end{malign}
\end{exampleblock}
\end{frame}