\begin{frame}
  \frametitle{Truth Tables and Properties of Formulas}

  \begin{center}
  \begin{tabular}{|c|c|c|c|c|}
    \hline
    \thd $p$ & \thd $q$ & \thd $\neg q$ & \thd $p \to \neg q$ & \thd $p \wedge (p \to \neg q)$ \\
    \hline
    $\F$ & $\F$ & \mpause[1]{$\T$} & \mpause[5]{$\T$} & \mpause[9]{$\F$}\\
    \hline
    $\F$ & $\T$ & \mpause[2]{$\F$} & \mpause[6]{$\T$} & \mpause[10]{$\F$}\\
    \hline
    $\T$ & $\F$ & \mpause[3]{$\T$} & \mpause[7]{$\T$} & \mpause[11]{$\T$}\\
    \hline
    $\T$ & $\T$ & \mpause[4]{$\F$} & \mpause[8]{$\F$} & \mpause[12]{$\F$}\\
    \hline
  \end{tabular}\\[.3ex]
  \mpause{\emph{contingency:} sometimes $\F$, sometimes $\T$}
  \end{center}
  \pause[15]%

  \begin{center}
  \begin{tabular}{|c|c|c|}
    \hline
    \thd $p$ & \thd $\neg p$ & \thd $p \vee \neg p$ \\
    \hline
    $\F$ & $\T$ & \mpause[1]{$\T$} \\
    \hline
    $\T$ & $\F$ & \mpause{$\T$} \\
    \hline
  \end{tabular}\\[.3ex]
  \mpause{\emph{tautology: } always $\T$}
  \end{center}
  \pause[19]%
  
  \begin{center}
  \begin{tabular}{|c|c|c|c|c|c|}
    \hline
    \thd $p$ & \thd $q$ & \thd $\neg p$ & \thd $p \to q$ & \thd $\neg(p \to q)$ & \thd $\neg p \wedge \neg( p \to q)$ \\
    \hline
    $\F$ & $\F$ & \mpause[1]{$\T$} & \mpause[5]{$\T$} & \mpause[9]{$\F$} & \mpause[13]{$\F$}\\
    \hline
    $\F$ & $\T$ & \mpause[2]{$\T$} & \mpause[6]{$\T$} & \mpause[10]{$\F$} & \mpause[14]{$\F$}\\
    \hline
    $\T$ & $\F$ & \mpause[3]{$\F$} & \mpause[7]{$\F$} & \mpause[11]{$\T$} & \mpause[15]{$\F$}\\
    \hline
    $\T$ & $\T$ & \mpause[4]{$\F$} & \mpause[8]{$\T$} & \mpause[12]{$\F$} & \mpause[16]{$\F$}\\
    \hline
  \end{tabular}\\[.3ex]
  \mpause{\emph{contradiction:} always $\F$}
  \end{center}
\end{frame}