Problem 2: Describe each of the following propositional functions on Z in succinct English with a minimum of symbols. Then find the truth sets of each. 1.) P(y) = “(x) (x < y)” 2.) Q(y) = “(x) (x<=y+ 5)” 3.) S(x) = “ (x>= 0) à (y) (x=y2)” Caution: quantifiers have higher operator precedence that logical operators, so this must be interpreted as “ (x>= 0) à [ (y) (x=y2) ]” Solution 1) P(y) = “(x) (x < y)” i.e. y must be greater than the domain i.e. all x values. 2) Q(y) = “(x) (x <= y + 5)” For any y, there exists x such that x-5 <=y maximum value x-5 can be y only. 3) S(x) = “ (x >= 0) à (y) (x = y2)” The curve x =y^2 for all x >0 Parabola open right..

1. Problem 2: Describe each of the following propositional functions on Z in succinct English with
a minimum of symbols. Then find the truth sets of each.
1.) P(y) = “(x) (x < y)”
2.) Q(y) = “(x) (x<=y+ 5)”
3.) S(x) = “ (x>= 0) à (y) (x=y2)”
Caution: quantifiers have higher operator precedence that logical operators, so this must be
interpreted as “ (x>= 0) à [ (y) (x=y2) ]”
Solution
1) P(y) = “(x) (x < y)”
i.e. y must be greater than the domain i.e. all x values.
2) Q(y) = “(x) (x <= y + 5)”
For any y, there exists x such that x-5 <=y
maximum value x-5 can be y only.
3) S(x) = “ (x >= 0) à (y) (x = y2)”
The curve x =y^2 for all x >0
Parabola open right.