Questionnaire-2024/predicate_logic/2001.tex

\item
  \ifassignmentsheet \point{1}
  \else \prac
  \fi
Consider the sentence $\phi = \exists x \forall y (P(x,y) \implies (Q(x,y) \lor R(x,y)))$.
Does the following model satisfy $\phi$?

The model $M$ consists of:
\begin{itemize}
\item  $A = \{a, b, c\} $
\item  $P^{M} = \{(a,a), (a,b), (b,a), (b,b), (c,a), (c,b)\}$
\item  $Q^{M} = \{(a,m) | m \in A \}$
\item  $R^{M} = \{(a,a), (b,a), (a,c), (b,c), (c,c)\}$
\end{itemize}


% \item The model $M'$ consists of:
%\begin{itemize}
%\item  $A = \mathbb{Z} $
%\item  $P^{M} = \{(m,n) | m \ge n \}$
%\item  $Q^{M} = \{(m,n) | m \le n \}$
%\item  $R^{M} = \{(m,n) | m = -n \}$
%\end{itemize}