1. 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 < y3

Q(x,y): x –1> y2

R(x,y,z): x + y3 > 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)

1. "x$y P(x,y)

2. $y"x P(x,y)

3. "y"x Q(x,y)

4. $y$x Q(x,y)