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  1. \item
  2. \ifassignmentsheet \points{3}
  3. \else \prac
  4. \fi
  5. 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.
  6. \begin{enumerate}
  7. \item \ifassignmentsheet \point{1} \fi $\forall x (P(x,x)) \lor \forall y (Q(x,y))$
  8. \item \ifassignmentsheet \points{2} \fi $\neg \forall x ((Q(f(x)) \implies P(f(f(x)))) \wedge \neg Q(x))$
  9. \end{enumerate}