Mathematics - Sets and Relations Question with Solution | TestHub

Both $R_1$ and $R_2$ are symmetric as For any $(x,y)\in R_1$, we have $(y,x)\in R_1$ and similarly for $R_2$ Now, for $R_2,(b,a)\in R_2,(a,c)\in R_2$ but $(b,c)\notin R_2$. Similarly, for $R_1,(b,c)\in R_1,(c,a)\in R_1$ but $(b,a)\notin R_1$. Therefore, neither $R_1$ nor $R_2$ is transitive.