The number of relations on the set A = 1,2,3 containing at most 6 elements including (1,2) , which are reflexive and transitive but not symmetric, is ________

Step-by-step solution

aligned & A= 1,2,3 & (1,1),(2,2),(3,3),(1,2) R aligned Remaining elements are (2,1),(2,3),(1,3),(3,1),(3,2) (1) If relation contains exactly 4 elements = 1 way (2) if relation contains exactly 5 elements It can be (1,3),(3,2) 2 ways (3) If relation contain exactly 6 elements It can be ((2,3),(1,3)),((1,3),(3,2)),((3,1),(3,2)) 3 ways. Total =6 ways