Chapter 17, Problem 1RE

To determine

Whether the statement “$x<-3\text{ or }x>1\text{ may also be written as }1<x<-3$” is true or false and explain the reason if the given statement is false.

Answer to Problem 1RE

The given statement is $\underset{\_}{\text{false}}$.

Explanation of Solution

Consider the inequality $1<x<-3$.

The given inequality $1<x<-3$ can be written as $1<x\text{ and }x<-3$ which is inconsistent.

Note that, if $1<x\text{ then }x\cancel{<}-3$ and if $x<-3\text{ then }x\cancel{<}1$, so the inequality $1<x<-3$ is inconsistent.

Therefore, the given statement is $\underset{\_}{\text{false}}$.