Translate each of these nested quantifications into an English statement that expresses a mathematical fact. The domain in each case consists of all real numbers.
- $\exists x \forall y (y=y)$
- $\forall x \forall y ((x>=0) \wedge (y<0)) \rightarrow (x-y>0)$
- $\exists x \exists y (((x<=0) \wedge (y<=0)) \wedge (x-y>0))$
- $\forall x \forall y ((x \neq 0) \wedge (y \neq 0) \leftrightarrow (xy \neq 0))$
