\item
  \ifassignmentsheet \points{3}
  \else \prac
  \fi
For each of the formulas of predicate logic below, find a model that satisfies the formula and one that does not. Draw a syntax tree and state all free variables.
    \begin{enumerate}
      \item \ifassignmentsheet \point{1} \fi $\forall x (P(x,x)) \lor \forall y (Q(x,y))$
      \item \ifassignmentsheet \points{2} \fi $\neg \forall x ((Q(f(x)) \implies P(f(f(x)))) \wedge \neg Q(x))$
    \end{enumerate}
