So im new to logic and i get really confused on quantifier scope and bound namely what variables occur free in a formula im currently stuck on this one.
$$\exists X. (\forall Y. F(X,Y)) \implies G(X, Y, Z)$$
I don't understand what the free variables are in this formula im certain that $Z$ is free but for the $ X $ and $Y$ in $$G(X, Y, Z)$$ im not sure if they are free or bound as they seem to occur outside of the existential quantifiers scope.
Some help would be greatly appreciated thanks in advance.