Chapter 1.5, Problem 31E

Express the negations of each of these statements so that all negation symbols immediately precede predicates.

a) $\forall x\exists y\forall zT\left(x,y,z\right)$

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

c) $\forall x\exists y\left(P\left(x,y\right)\wedge \exists zR\left(x,y,z\right)\right)$

d) $\forall x\exists y\left(P\left(x,y\right)\to Q\left(x,y\right)\right)$