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  1. \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.
  2. \begin{enumerate}
  3. \item $\forall x \exists y \; \big( P(f(y))~\land~P(x) \big) ~\imp~Q(f(f(y)))$
  4. \end{enumerate}