1. (15 points) In our first lecture we have seen that for any set X, a binary relation ~ is a subset of X x X. In each of the following cases, determine whether the binary relations are reflexive, irreflexive, symmetric, asymmetric, transitive and complete. You will have to argue which of these 6 properties, the relation satisfies. (a) (5 points) X = {1, 2,3} and ~= { (1, 1)(1, 2), (2, 2), (1,3), (2, 3), (3, 1), (3,3) ] (b) (5 points) X = R', and > is the "greater than or equal to" relation > (c) (5 points) X = R , and ~ is the following relation: > > y if |x - y|