\item For each of the formulas in predicate logic below, find a model that satisfies the formula and one that does not. Draw a syntax tree and state all free variables while solving this task.
\begin{enumerate}
    \item $\neg\forall x ((P(x) \implies P(y)) \land P(x))$
    \item $\forall x \exists y (P(x,y) \land \neg P(f(x),f(y)))$
\end{enumerate}