$$\exists y \forall xP(x, y) \equiv \forall x \exists yP(x,y)\tag{1}$$ $$\exists y \forall x(P(x) \lor Q(y)) \equiv \forall x P(x) \lor \exists x Q(x)\tag{2}$$
$$\exists x(P(x) \lor Q(x)) \equiv \exists xP(x)\lor \exists yQ(y)\tag{3}$$
Without proving them is there a way to quickly know whether it is true or not?