4. (10 pt., 2.5 pt. each) Let A = P(0), B = P({a, b), and C =P((a,c)) where P(S) is the power set of S. Find: a. A, B, and C b. AnB d. (B - C)nA Part II: Relations (50 pt.) 1. (50 pt., 10 pt. each) For each of the following relations, determine whether the relation is: Reflexive. Anti-reflexive Symmetric. Anti-symmetric. Transitive. Justify your answers a. R is a relation on the set { 1, 2, 3, 4} such that R = {(1, 1), (1, 3), (2,2), (3, 1), (3, 3), (4,4). b. R is a relation on the set of all people such that (a, b) E R if and only if a and b have a common grandparent. R is a relation on the power set of a set A such that (x, y) E R if and only if x cy. R is a relation on Z such that (x,y) E R if and only if x # y. R is a relation on Z+ such that (x, y) e R if and only if y is divisible by x. Hint: An integer y is divisible by an integer x with x # 0 if and only if there exists an integer k c. d, e. such that y-xk