\begin{frame} \frametitle{Examples Semantic Entailment} \begin{exampleblock}{} Do we have \quad $p \to q, \; \neg q \;\models\; \neg p$ \quad ? \pause \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline \thd $p$ & \thd $q$ & \thd $p \to q$ & \thd $\neg q$ & \thd $\neg p$ \\ \hline $\F$ & $\F$ & \malert{2}{3}{$\T$} & \malert{2}{3}{$\T$} & $\T$\\ \hline $\F$ & $\T$ & $\T$ & $\F$ & $\T$\\ \hline $\T$ & $\F$ & $\F$ & $\T$ & $\F$\\ \hline $\T$ & $\T$ & $\T$ & $\F$ & $\T$\\ \hline \end{tabular} \end{center} \pause At which line(s) do we need to look? \begin{itemize} \pause \item where both $p \to q$ and $\neg q$ are $\T$ \end{itemize} \pause\medskip In this line(s) $\neg p$ is true. \bigskip \pause Hence $p \to q, \; \neg q \;\models\; \neg p$ holds. \end{exampleblock} \end{frame}