मान लीजिए कि $A =\{1,2,3\}$ है। तब सिद्ध कीजिए कि ऐसे संबंधों की संख्या चार है, जिनमें $( 1,2)$ तथा $(2,3)$ हैं और जो स्वतुल्य तथा संक्रामक तो हैं किंतु सममित नहीं हैं।

The smallest relation $R_{1}$ containing $(1,2)$ and $(2,3)$ which is reflexive and transitive but not symmetric is $\{(1,1),\,(2,2),\,(3,3),$ $(1,2),\,(2,3),\,(1,3)\} .$ Now, if we add the pair $(2,1)$ to $R_{1}$ to get $R_{2}$, then the relation $R_{2}$ will be reflexive, transitive but not symmetric. Similarly, we can obtain $R _{3}$ and $R _{4}$ by adding $(3,2)$ and $(3,1)$ respectively, to $R_{1}$ to get the desired relations. However, we can not add any two pairs out of $(2,1),$ $(3,2)$ and $(3,1)$ to $R_{1}$ at a time, as by doing so, we will be forced to add the remaining third pair in order to maintain transitivity and in the process, the relation will become symmetric also which is not required. Thus, the total number of desired relations is four.