Consider the following digraph that represents a relation R on a set of points X = {a, b, c, d}. (a) Write out the elements of R. (b) Is R an equivalence relation? If it is not, which property or properties fail to hold? Suppose that a relation R on a set X is a partial order (i.e., R is reflexive, antisymmetric, and transitive). Recall that the inverse of R, denoted by R^-1, is defined by R^-1 = {(y, x): (x, y) elementof R}. Show that R^-1 is also a partial order on X (i.e., R^-1 is also reflexive, antisymmetric, and transitive)