Question

Check whether the relation $R$ in the set $\{1,2,3\}$ given by $R=\left\{\right(1,2),(2,1)$ is transitive.

Answer 1

For transitive $\Rightarrow \left(0,b\right)\in R\Rightarrow \left(b,c\right)\in RSo\left(a,c\right)\in R$

$\begin{array}{c}R=\left\{\left(1,2\right)\left(2,1\right)\right\}\\ So\left(a,b\right)=\left(1,2\right)\Rightarrow \left(b,c\right)=\left(2,1\right)Then\left(1,1\right)\&R\end{array}$

So we say In R has only two elements $(1,2)(2,1)$ & $(1,1)$ is not present in R.

So it is not Transitive.