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