(a) All you know about two sets S and T is that they are subsets of the universal set U = {1, 2, 3, 4, 5, 6}, and that |S| = 5 and |T| = 3. What are all of the different possible values of |P(S T)|, the size of the power set of the intersection of S and T?

(b) Determine, with explanation, whether the following statement is true or false: x Z, dx 0.5e bxc

(c) Let R be the relation on the set S = Z given by R = {(a, b) | a b = 1}. Determine, with explanation, whether R is transitive.