Let R be the domain of the predicate variable x. Which of the following are true and

Chapter 3, Problem 32

(choose chapter or problem)

Let R be the domain of the predicate variable x. Which of the following are true and which are false? Give counter examples for the statements that are false.

a. \(x>2 \Rightarrow x>1\)

b. \(x>2 \Rightarrow x^{2}>4\)

c. \(x^{2}>4 \Rightarrow x>2\)

d. \(x^{2}>4 \Leftrightarrow|x|>2\)

Text Transcription:

x>2 Rightarrow x>1

x>2 Rightarrow x^2 >4

x^2 >4 Rightarrow x>2

x^2 >4 Leftrightarrow |x|>2