I'm working with the universal and the existential quantifiers and I was wondering is there an order of operations that applies to them? What is the difference between
$(\forall x)P(x)(\exists x)Q(x)$
And
$(\exists x)Q(x)(\forall x)P(x)$
Lets say we have this relationship
(a) $[(\forall x)P(x) \vee (\exists x)Q(x)] \implies (\forall x)[P(x) \vee Q(x) ]$