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\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.
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