a) Suppose that $\displaystyle {X_n}$ and $\displaystyle {Y_n}$ converge to the same point. Prove that $\displaystyle {X_n} - {Y_n} \rightarrow 0$ as $\displaystyle n \rightarrow \infty$.

b) Show the converse is false.

Again as usual... some kind of explanation to help me understand this helps alot... :)