\begin{frame}
  \frametitle{Logic Equivalence}

  \begin{goal}{}
    Formulas $\phi$ and $\psi$ are \emph{logically equivalent}, denoted
    \begin{talign}
      \phi \;\equiv\; \psi\;,
    \end{talign}
    if $\phi$ and $\psi$ have the same truth table.
  \end{goal}
  \smallskip
  
  \begin{center}
  \begin{tabular}{|c|c|c|c|c|}
    \hline
    \thd $p$ & \thd $q$ & \thd $\neg p$ & \thd $\neg p \vee q$ & \thd $p \to q$ \\
    \hline
    $\F$ & $\F$ & $\T$ & \malert{1}{2}{$\T$} & \malert{1}{2}{$\T$}\\
    \hline
    $\F$ & $\T$ & $\T$ & \malert{1}{2}{$\T$} & \malert{1}{2}{$\T$}\\
    \hline
    $\T$ & $\F$ & $\F$ & \malert{1}{2}{$\F$} & \malert{1}{2}{$\F$}\\
    \hline
    $\T$ & $\T$ & $\F$ & \malert{1}{2}{$\T$} & \malert{1}{2}{$\T$}\\
    \hline
  \end{tabular}\\
  \medskip
  \mpause[2]{\quad\quad \alert{$\neg p \vee q \;\equiv\; p \to q$}}
  \end{center}
  \vspace{-1ex}
  \pause[4]
  
  \begin{exampleblock}{More examples}
    \begin{malign}
      p \wedge q \;&\equiv\; \neg (\neg p \vee \neg q)  
      \\
      p \vee q \;&\equiv\; q \vee p
      \\
      p \to \neg q \;&\equiv\; q \to \neg p
    \end{malign}
  \end{exampleblock}
\end{frame}