Let $\displaystyle (M_1,d_1)$ and $\displaystyle (M_2,d_2)$ be metric spaces and let $\displaystyle f:M_1 \rightarrow M_2$ be a continuous surjective map such that $\displaystyle d_1(p,q) \leq d_2(p,q)$ for evey $\displaystyle p,q \in M_1$.

a)If $\displaystyle M_1 $ is complete, is $\displaystyle M_2$ complete?

b)If $\displaystyle M_2$ is complete, is $\displaystyle M_1 $ complete?