\begin{frame}
  \frametitle{Examples Semantic Entailment}
  
  \begin{goal}{}
    To show that $\alpha_1,\ldots,\alpha_n \;\models \; \beta$ we need to show 
    \begin{itemize}
      \item $\beta$ is true whenever $\alpha_1,\ldots,\alpha_n$ are true.
    \end{itemize}
    \pause
    This can also be achieved by logical reasoning:
    \begin{itemize}
      \item assume that $\alpha_1,\ldots,\alpha_n$ are true, and
      \item show that $\beta$ must be true as well.
    \end{itemize} 
  \end{goal}
  \pause
  
  \begin{exampleblock}{}
    Do we have \quad $p \to q, \; \neg q \;\models\; \neg p$ \quad ?
    \pause
    \bigskip
    
    Assume that $p \to q$ and $\neg q$ are $\T$.
    \medskip\pause
    
    Then $q$ is $\F$.
    \medskip\pause
    
    Then $p$ must be $\F$ since otherwise $p \to q$ was $\F$.
    \medskip\pause

    Thus $\neg p$ is $\T$.    
    \bigskip\pause
    
    Hence $p \to q, \; \neg q \;\models\; \neg p$ holds.
  \end{exampleblock}
\end{frame}