question_answer 3)

Check whether the relation R defined in the set {1,2, 3,4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.  

Answer:

t A = {1, 2, 3, 4, 5. 6}     R = {(a, b) : b = a + 1, a, b A}.                R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)}.  Reflexive : As 1 e A and (1, 1)  R             R is not reflexive.        Symmetric : As 2, 3 A and (2, 3) R. But             R is not symmetric,     Transitive : As 2. 3 and 4  A and (2, 3) R, (3,   t (2,4) R '          R is not transitive. Hence R is neither reflexive, nor symmetric, nor               transitive.