Chapter 1.3, Problem 10E

Which of the following are true in the universe of all real numbers?
(a) $(\forall x)(\exists y)(x+y=0)$ .
(b) $(\exists x)(\forall y)(x+y=0)$ .
(c) $(\exists x)(\exists y)(x^{\text{2}}+y^{\text{2}}=-\text{1})$ .
(d) $(\forall x)[x>0\Rightarrow (\exists y)(y<0\wedge xy>0)]$ .
(e) $(\forall y)(\exists x)(\forall z)(xy=xz)$ .
(f) $(\exists x)(\forall y)(x\le y)$ .
(g) $(\forall y)(\exists x)(x\le y)$ .
(h) $(\exists !y)(y<0\wedge y+\text{3}>0)$ .
(i) $(\exists !x)(\forall y)(x=y^{\text{2}})$ .
(j) $(\forall y)(\exists !x)(x=y^{\text{2}})$ .
(k) $(\exists !x)(\exists !y)(\forall w)(w^{\text{2}}>x-y)$ .