First-order prefixes

Quote:

Explain the difference between the first-order prefixes:
(a) $\exists x\forall y$ and $\forall x\exists y$ ;
(b) $\exists x\forall y\exists z$ and $\forall x\exists y\forall z$ ;
(c) $\forall x\exists y\forall z\exists w$ and $\exists x\forall y\exists z\forall w$ .

First, I notice that each prefix can be obtained by negation from the other one in the pair. Also, I can show a formula such that different prefixes produce different truth values. For example, consider (c):
$\forall x\exists y\forall z\exists w(x+z=y+w)$ is true, but $\exists x\forall y\exists z\forall w(x+z=y+w)$ is false. I ask whether I missed something.