Chapter 0.1, Problem 2E

Classify each of the following statements as true, false, or not valid mathematical statement. Explain your answers.

$4=2+2$ and $7<\sqrt{50}$.

$4\ne 2+2$ and $7<\sqrt{50}$.

$5$ is an even number and ${16}^{-1/4}=\frac{1}{2}$.

$5$ is an even number or ${16}^{-1/4}=\frac{1}{2}$.

$9=3^2$ or $3.14<\pi$.

${\sqrt{3}}^{\sqrt{3}}$ is rational or ${\left(-4\right)}^2=16$.

$4=2+2\to 7<\sqrt{50}$.

$2$ is an even integer $\to$ 6 is an odd integer.

Let $n$ denote a positive integer.

$4=2+2\leftrightarrow 7<\sqrt{50}$

$4\ne 2+2\to 7<\sqrt{50}$

$4\ne 2+2\leftrightarrow 7<\sqrt{50}$

$4=2+2\to 7>\sqrt{50}$

The area of the circle of radius $r$ is $2\pi r$ or its circumference is $\pi r^2$.

$2+3=5\to 5+6=10$

If $a$ and $b$ are integers with $a-b\ge 0$ and $b-a\ge 0$, then $a=b$.

If $a$ and $b$ are integers with $a-b>0$ and $b-a>0$, then $a=b$.