Why are the following not logically equivalent? Why are the following statements not logically equivalent? 
$$((\forall x\in D,P(x))\vee(\forall x\in D, Q(x))$$
and $$\forall x\in D, (P(x)\vee Q(x)$$
I have thought for several hours about this and I can't think of any reason why they shouldn't be equivalent. May someone help me?

Because if, for example, each $x$ satisfies $P$ or $Q$ but not both, with both cases occurring, the first statement is false but the second one is true.
