"The set of rational number is closed under division. -- TRUE OR FALSE" I think this is false, but simply cause I read it in my text book (or mis-read it if I am wrong).
If $\displaystyle \left\{ {n,m} \right\} \subseteq \mathbb{Q}\quad \& \quad n \ne 0$ then what can you say about $\displaystyle \frac{m}{n}$?
What happens if that ratio is not rational?
Good grief, if that is true, what do you know? What do you know about rational numbers? Are you trying to get a completely solved, ready to turn in solution?