\item \lect For the following formula in \textit{Predicate Logic}, find a \textit{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 $\forall x \exists y \; \big( P(f(y))~\land~P(x) \big) ~\imp~Q(f(f(y)))$
\end{enumerate}