Mathematics - Sets and Relations Question with Solution | TestHub

We know that $(x, y)\in \mathrm{R} , (\mathrm{y}, \mathrm{x})\in \mathrm{R} \Rightarrow$symmetric

$(x, y)\in \mathrm{R} , (\mathrm{y}, z)\in \mathrm{R} \& (z, x)\in \mathrm{R}\Rightarrow$transitive
$\left.\begin{array}{l}0<|x-y|\le 1\\ 0<|y-x|\le 1\end{array}\right\}$is symmetric

let 

$0<|x-y|\le 1$                                         .......(1)
$(1,2)\in \mathrm{R}$ and $(2,3)\in \mathrm{R}$ satisfy the equation (1)
but $(1,3)\notin R$ not satisfied
Hence $0<|x-y|\le 1$ is symmetric but not transitive relation