\begin{frame}{Exercise}
  \begin{exampleblock}{}
    \begin{malign}
      S &\to AAc &
      A &\to Ba\mid \lambda &
      B &\to Ab\mid d
    \end{malign}
    \pause\vspace{-1ex}
    
    The erasable variables ($V \Rightarrow^+ \lambda$) are: \pause $A$\;.
    \pause\medskip
    
    We determine \( \text{PreFirst}(A) \), \( \text{PreFirst}(B) \) and \(\text{PreFirst}(S) \):\pause
    \begin{talign}
      \text{PreFirst}(A) &= \{\, 
        \mpause[1]{A}
        \mpause{, \underbrace{Ba}_{\text{from $A$}}}
        \mpause{, \underbrace{\lambda}_{\text{from $A$}}}
        \mpause{, \underbrace{B}_{\text{from $Ba$}}}
        \mpause{, \underbrace{Ab}_{\text{from $B$}}}
        \mpause{, \underbrace{d}_{\text{from $B$}}}
        \mpause{, \underbrace{b}_{\text{from $Ab$}}}
      \,\} \\
      \text{PreFirst}(B) &= \{\, 
        \mpause{B}
        \mpause{, \underbrace{Ab}_{\text{from $B$}}}
        \mpause{, \underbrace{d}_{\text{from $B$}}}
        \mpause{, \underbrace{b}_{\text{from $Ab$}}}
        \mpause{, \underbrace{A}_{\text{from $Ab$}}}
      \,\} \mpause{\cup \text{PreFirst}(A)} \\
      &\mpause{= \{\, A, Ba, \lambda, B, Ab, d, b \,\}}
      \\
      \text{PreFirst}(S) &= \{\, 
        \mpause{S}
        \mpause{, \underbrace{AAc}_{\text{from $S$}}}
        \mpause{, \underbrace{Ac}_{\text{from $AAc$}}}
        \mpause{, \underbrace{c}_{\text{from $Ac$}}}
        \mpause{, \underbrace{A}_{\text{from $AAc$}}}
      \,\} \mpause{\cup \text{PreFirst}(A)} \\
      &\mpause{= \{\, S, AAc, Ac, c, A, Ba, \lambda, B, Ab, d, b \,\}}
    \end{talign}
    \smallskip
    \mpause{
    Thus we get
    \begin{malign}
      \text{First}(A) &= \mpause{\{\, b, d, \lambda \,\}} &
      \text{First}(B) &= \mpause{\{\, b, d \,\}} &
      \text{First}(S) &= \mpause{\{\, b, c, d \,\}}
    \end{malign}
    }
  \end{exampleblock}
\end{frame}

\themex{$\follow{A}$}