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 ______. 

Transitivity $(1,2)\in \mathrm{R},(2,3)\in \mathrm{R}\Rightarrow (1,3)\in \mathrm{R}$
For reflexive $(1,1),(2,2)(3,3)\in \mathrm{R}$
Now (2, 1), (3, 2), (3, 1) 
(3, 1) cannot be taken 
(1) (2, 1) taken and (3, 2) not taken 
(2) (3, 2) taken and (2, 1) not taken 
(3) Both not taken 
therefore 3 relations are possible.