Let A= 1,2,3 . The number of relations on A , containing (1,2) and (2,3) , which are reflexive and transitive but not symmetric, is ______ -

Step-by-step solution

R is reflexive R have (1,1),(2,2),(3,3)R is transitive aligned & (1,2),(23) R (1,3) R & R₁= (1,1),(2,2),(3,3),(1,2),(2,3),(1,3) aligned Clearly R₁ is reflexive and transitive but not symmetric. Similarly, aligned & R₂= (1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(3,2) & R₃= (1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(2,1) aligned Therefore, 3 relations are possible