Solved: In 2830, rewrite each statement without using quantifiers or variables. Indicate

Chapter 3, Problem 28

(choose chapter or problem)

In 28–30, rewrite each statement without using quantifiers or variables. Indicate which are true and which are false, and justify your answers as best as you can.

Let the domain of x be the set D of objects discussed in mathematics courses, and let Real(x) be “x is a real number,” Pos(x) be “x is a positive real number,” Neg(x) be “x is a negative real number,” and Int(x) be “x is an integer.”

a. Pos(0)

b. \(\forall x, \operatorname{Real}(x) \wedge \operatorname{Neg}(x) \rightarrow \operatorname{Pos}(-x)\).

c. \(\forall x, \operatorname{Int}(x) \rightarrow \operatorname{Real}(x)\).

d. \(\exists x \text { such that } \operatorname{Real}(x) \wedge \sim \operatorname{Int}(x)\).

Text Transcription:

forall x, Real(x) wedge Neg(x) rightarrow Pos(-x)

forall x, Int(x) rightarrow Real(x)

exists x such that Real(x) wedge sim Int(x)