Overview
#1. The distinction between ? and ?. Recall that for sets A and B, A ? B means that A is a subset of B. Recall also that x ? C means that x is an element of C. Also, y /? D means that y is not an element of D. Let ? denote the empty set. (
1a) We have already proved that ? ? A for any set A. However, ? ? ? / ; explain why.
(1b) Explain why ? ? P(X) for any set X, where P(X) is the power set of X.
(1c) Let U be the universal set. Suppose that A and B are sets. Explain why A ? B ? P(A), where A ? B is the set difference of A and B. (1d) It is possible for x, A, and B to be such that x ? A and A ? B. Given an example. (1e) It is possible that both A ? B and A ? B. Given an example.