(a) Let F be a collection of open sets in $\displaystyle R^n$. Prove that U F (i.e. the union of all of the sets in F) is always an open set in $\displaystyle R^n$.

(b) Let F be the collection of closed intervals $\displaystyle A_n$=[1/n, 1-1/n] for n=1,2,3,.... What do you notice about U F? Is it closed, open, both or nither?