4. (30 pt., 6 pt. each) For each of the following relations, determine whether the relation is: Reflexive. Anti-reflexive Symmetric. e Transitive. A partial order. . A strict order. Anti-symmetric. An equivalence relation. a. 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. b. R is a relation on the power set of a set A such that (X, Y) E R if and only if XcY. c. R is a relation on Z such that (x, y) E R if and only if lx-yl s 2. d. R is a relation on Z+ such that (x, y) E R if and only if there is a positive integer n such that x-y e. R is a relation on R such that (x, y) E R if and only if x - y is rational. Hint: The sum of two rational numbers is rational