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

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

Does the model $\mathcal{M}$ satisfy the formula $\phi$?
Explain your answer by drawing a \textbf{syntax tree} and evaluate the model $\mathcal{M}$ with the help of this syntax tree.