1.27)    In each case, a relation on the set {1,2,3} is given. Of the three properties,
                    reflexivity, symmetry, and transitivity, determine which ones the relation has.
                    Give reasons for each of them.
                    (a)    R = { (1,3), (3,1), (2,2) }.
                    (b)    R = {(1, 1), (2,2), (3, 3), (1, 2)}.

           Solution:
                    a)
                        It is Symmetry.
                            Because whever there is something like (a, b) we also have (b, a).
                            Here it is (1, 3) we also have (3, 1) and (2, 2).

                    b)
                        It is reflexive
                            Because for every 'a' we have (a, a).
                            Here it is (1, 1), (2,2), (3, 3)