\begin{frame}
  \frametitle{Exercises}
  
  Meaning of the symbols:
  \begin{talign}
    a: \quad& \text{Alice} &
    L(x,y): \quad & \text{$x$ likes $y$}
  \end{talign}
  Translate the following sentences into predicate logic:
  \bigskip
  
  \begin{alertblock}{}
    Everybody likes at most 2 \textit{other} people.
  \end{alertblock}
  \pause\bigskip

  Note that \emph{at most} means that it can be $0$, $1$ or $2$ !
  \pause\bigskip
  
  \begin{exampleblock}{}
    \vspace{-1.5ex}
    \begin{talign}
      \myall{x}{\myex{y_1}{\myex{y_2}{\myall{z}{
        \big(\; L(x,z) \wedge z \ne x \;\to\; z = y_1 \vee z = y_2 \;\big)
      }}}}
    \end{talign}
  \end{exampleblock}
  \pause\smallskip
  
  or, equivalently
  
  \begin{exampleblock}{}
    \vspace{-1.5ex}
    \begin{talign}
      \myall{x}{\myall{y_1}{\myall{y_2}{\myall{y_3}{
        \big(\; &L(x,y_1) \wedge L(x,y_2) \wedge L(x,y_3) \\
                &\wedge x \ne y_1 \wedge x \ne y_2 \wedge x \ne y_3 \\
                &\quad\to y_1 = y_2 \vee y_2 = y_3 \vee y_1 = y_3 \;\big)
      }}}}
    \end{talign}
  \end{exampleblock}

  \vspace{10cm}
\end{frame}