1. Let A1, . . . ,An be subsets of a (nonempty, but not necessarily finite) set

.

(For partial credit, you may consider just the case n = 2.)

(a) Let f be the collection of nonempty subsets of

of the form

C = X1 ^X2^...^ Xn : ,Xi = Ai or Xi = Ai(complement)

Show that f is a partition of

.

(b) Show that the collection F of (necessarily finite) unions of zero or more cells

of f is the smallest field of subsets of

which contains each of A1, . . . ,An.

(c) Use this result to do Problem 2 from Assignment 1.

It is my assignment, I am really confused about it