Can somebody explain to me (in fool's english) why or why not the union of an open set and a closed set is open, closed, neither or both?

What aboutZ? What aboutQ?

...

[0,1] U [2,3] U [4,5] U ... U [2n, 2n + 1] U ...

I assume this is an infinite collection of closed sets. Great.

If the union of a finite collection of closed sets inRis closed... does that mean this is open?