proof for bipartite graphs

Let G be a bipartite graph with vertex partition { $V_1, V_2$}.

a)Prove that:

$\sum_{x \exists V_1}\deg(x) = |E| = \sum_{y \exists V_2}\deg(y)$

b) A graph is $k-regular$ if every vertex has degree $k$. Prove that if $G$ is $k-regular$ with $k > 0$, then $|V_1| = |V_2|$ (NOTE: G is bipartite with vertex partition { $V_1, V_2$}.)