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 = R2, and ~ is the "greater than or equal to" relation > (c) (5 points) X = R , and ~ is the following relation: x _ y if (x - y|