For Problem B-5:

The following statements are equivalent:

(1)	$x > 0$
(2)	$x \neq 0$ and ${\frac{\displaystyle 1}{\displaystyle x}} > 0$
(3)	$x = y^2$ for some real number $y$ with $y \neq 0$

Also, the following statements are equivalent:

(1)	$x^2 > 0$
(2)	$x \neq 0$