Part Ill: Relations (50 pt.) (30 pt, 5 pt. each) For each of the following relations, determine whether the relation is . A partial order .A striet order . Reflexive Ant-reneriv . Symmetric . Anti-symmetric A total order. . An equivalence relation Transitive a. RIs a relation on the set (1. 2. 3. 4} such that R-((1, 1), (1.2), 0.1). (2.2),(3,3), (4,4)). b. R is a relation on the set of all people such that (a. b) R If and only if a and b have a c. R is a relation on the power set of a set A such that (x. y) R if and only if xcy d. R is a relation on Z' such that (x. y) E R if and only if x divides y e. Risarelation on z such that (x,y) E R if and only if r # y. t. R is a relation on Z such that (x, y) E R If and only if xy 21