Compact spaces - Union and Intersection

Hey guys, i hope you can help me.

I have to prove that if $\displaystyle K_1, K_2,..., K_n$ are all compact subsets of the metric space $\displaystyle (X,d)$:

a) $\displaystyle K_1 \cap K_2\cap K_3 \cap... \cap K_n$ is compact.

b) $\displaystyle K_1 \cup K_2 \cup K_3 \cup ... \cup K_n$ is compact.

Im really kind of stuck on this, and ive been working on it for quite some time. Any of you guys who can tell me what to do or point me in the right direction?

Thanks a lot.

Morten