Consider the formula

A $=($x $$z $($P$($x$)$ Q$($y$,$ f$($z$))))($x P$($y$)$ Q$($f$($x$),$ z$)).$

$($a$)$ Draw the tree representation of A$.$

$($b$)$ Identify all bound variables and free variables in A$.$ Does there exist any variable in A that has

both bound and free occurrences?

$($c$)$ Give the resultant formula after performing the substitution A$[$y$/$f$($x$)].$ Is f$($x$)$ free for y in A$?$