\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}