For each of the following:

i. Write/expand each of the following predicates using disjunctions, conjunctions, and negations.

ii. Determine the truth value of the following statements.

Given:

P(x,y): x < y^3

Q(x,y): x –1 > y^2

R(x,y,z): x + y^3 > z

Universe of discourse for variable x isN(natural numbers)

Universe of discourse for variable y is Z+ (positive integers)

Universe of discourse for variable z is R+ (positive real numbers)

a. $\displaystyle \forall x \exists y P(x,y)$

b. $\displaystyle \exists y \forall x P(x,y)$

c. $\displaystyle \forall y \forall x Q(x,y)$

d. $\displaystyle \exists y \exists x Q(x,y)$

I understand the problem except that in the discrete book the problems always give a set of particular numbers to use the conjunctions, disjunctions, and negations on.