\item \lect Given the formula $$\phi = \forall x \exists z \; \big( \lnot P(x) \lor Q(y, f(z))\big) \imp \big( \exists x \; P(y) \land Q(f(x), z)\big),$$ construct a syntax tree for $\phi$ and determine the \textit{scope} of its quantifiers and which occurrences of the variables are \textit{free} and which are \textit{bound}.