(a)Give an example of two metric spaces $\displaystyle (X_{1}, d_{1})$ and $\displaystyle (X_{2}, d_{2})$ which are topologically equivalent and for which $\displaystyle (X_{1}, d_{1})$ is complete and $\displaystyle (X_{2}, d_{2})$ is not.

(b)Give an example of a set X with two equivalent metrics d and d' for which (X, d) is complete and (X, d') is not.