Suppose that D and E are sets, and D ? E. Let A = P(E). Recallthat P(E) denotes the set of all subsets of E. Define a relation Ron A by
R = {(X, Y) ? A × A: [(X ? Y) ? (Y ? X)] ? D}. So, XRY if andonly if [(X?Y) ? (Y ?X)] ? D.
Prove that R is an equivalence relation on A.
