51. (3): Let we have set $A = \{ 1,2,3\}$ \end{enumerate} By definition, we can say that\\ For reflexivity ; $(1,1)(2,2)$ and $(3,3) \in R$\\ For symmetry $;(2,1)(1,2) \in R$\\ For transitivity $(1,2) \in R$ and $(2,3) \in R \Rightarrow (1,3) \in R$ But according to the question, For not symmetric $;(2,1)$ and $(3,2) \notin R$\\ So, $R_{1} = \{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}$\\ $R_{2} = \{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)(2,1)\}$ and $R_{3} = \{(1,1),(2,2),(3,3),(1,2)(2,3)(1,3)(3,2)\}$ \begin{enumerate} \def\labelenumi{\arabic{enumi}.} \setcounter{enumi}{45}