Let B be the collection of subsets of R of the form [a,b) for a<b, nulset, and the whole set R.

Show that if A and C are elements of B then A intersect B is in B.

and

Show that if {A_i| 0 <= i <= n} is a finite collection of subsets of B then the collection of intersections (from i=1 to n) of A_i is in B.

I'm not really sure how to go about this. Any help would be great. Thanks!!