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\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}