Chapter 1.5, Problem 30E

Rewrite each of these statements so that negations appear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives).

a) $\neg \exists y\exists xP\left(x,y\right)$

b) $\neg \forall x\exists yP\left(x,y\right)$

c) $\neg \exists y\left(Q\left(y\right)\wedge \forall x\neg R\left(x,y\right)\right)$

d) $\neg \exists y\left(\exists xR\left(x,y\right)\vee \forall xS\left(x,y\right)\right)$

e) $\neg \exists y\left(\forall x\exists zT\left(x,y,z\right)\vee \exists x\forall zU\left(x,y,z\right)\right)$