Let A1,..... An be arbitrary subsets of an abstract set (, and let A'i be either Ai

Question:

Let A1,..... An be arbitrary subsets of an abstract set (, and let A'i be either Ai or Aci, i = 1,.... n. Define the class C of subsets of ( as follows:
C = {all unions of the intersections A'1 (...( A'n}.
Then show that
(i) The class C is a field (generated by the sets A1,...., An).
(ii) Compute the number of elements of C.