Let $R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}$ be a relation on the set $A=\{1,2,3,4\}.$ The relation $R$ is

To determine the nature of the relation $R$ on set $A=\{1,2,3,4\}$:Function: A relation is a function if every element in the domain has a unique image. Here, the element $2$ is related to both $4$ and $3$ ($(2,4)\in R$ and $(2,3)\in R$), so it is not a function.Reflexive: For $R$ to be reflexive, $(a,a)\in R$ for all $a\in A$. Since $(1,1)\notin R,$ it is not reflexive.Symmetric: For $R$ to be symmetric, $(a,b)\in R$ must imply $(b,a)\in R$. In this relation, $(2,3)\in R$ but $(3,2)\notin R$. Therefore, the relation is not symmetric.Transitive: For $R$ to be transitive, $(a,b)\in R$ and $(b,c)\in R$ must imply $(a,c)\in R$. Here $(4,2)\in R$ and $(2,3)\in R,$ but $(4,3)\notin R,$ so it is not transitive.