\item
  \ifassignmentsheet \points{2} \fi
Given is the following formula in predicate logic
$$\phi = \exists x \forall y \Bigl(
\bigl(
P(x,y) \implies Q(x,y)
\bigr)
\vee
\bigl(
P(y, x)  \implies R(x,y)
\bigr)
\Bigr) $$
and the model $\mathcal{M}$:

\begin{itemize}
\item  $\mathcal{A} = \{a, b\} $
\item  $P^{M} = \{(a,b), (b,b), (b,a)\}$
\item  $Q^{M} = \{(a,a)\}$
\item  $R^{M} = \{(b,b)\}$
\end{itemize}

Does the model $\mathcal{M}$ satisfy the formula $\phi$?
Evaluate $\Model$ using a syntax tree.