On Z, the set of integers, define a relation R on Z as follows:  aRb   if  ab≥0 then

For each a∈Z,aRa as a2≥0R is reflexive.  Next, if a R b, then ab≥0⇒ ba≥0⇒bRa⇒R is symmetric.Next, supposea=-1, b = 0, c = 8 Then a R b as ab ≥ 0 and b R c as bc ≥ 0 but a is not related  to c as ac =-8 < 0. Thus, R is reflexive, symmetric but not transitive