HW for $4\mathrm{.}8$ :

Determine which statements are true and which are false. Prove those that are true and disprove those that are false.

$8-5\sqrt[\phantom{2}]{2}$ is irrational.

The difference of any two irrational numbers is irrational.

If $r$ is any rational number and $s$ is any irrational number, then $\frac{r}{s}$ is irrational.