Chapter 5.CR, Problem 21CR

To determine

a.

To classify:

The statement “$\left|x\right|$ always is positive” as true or false.

To determine

b.

To classify:

The statement “For all $x$ and $y$, $\left|x+y\right|=\left|x\right|+\left|y\right|$” as true or false.

To determine

c.

To classify:

The statement “For all integers $a$ and $b$, if $a{\text{ < }}^{-}b$ then $a<0$” as true or false.

To determine

d.

To classify:

The statement “For all $x$ and $y$, ${\left(x-y\right)}^2={\left(y-x\right)}^2$” as true or false.