question_answer 6)

Show that the relation R is the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive. 

Answer:

Let A = {1, 2, 3} : R = {(1, 2), (2, 1)}       Reflexive : As  and (1, 1)        is not reflexive.       Symmetric : As 1, 2  and (1, 2)       (2, 1),        is symmetric       Transitive : As (1, 2)  and (2, 1)       But (1, 1)        R is not transitive.