Question

State the reason for the relation R on the set {1, 2, 3} given by R = {(1, 2), (2, 1)} to be transitive.

Answer 1

$$\begin{gathered} \mathrm{Since}\left(1,2\right)\in R,\left(2,1\right)\in R\mathrm{but}\left(1,1\right)\notin R,R\mathrm{is}\mathrm{not}\mathrm{transitive}\mathrm{on}\mathrm{the}\mathrm{set}\left\{1,2,3\right\}. \\ \mathrm{For}R\mathrm{to}\mathrm{be}\mathrm{in}\mathrm{a}\mathrm{transitive}\mathrm{relation},\mathrm{we}\mathrm{must}\mathrm{have}\left(1,1\right)\in R. \end{gathered}$$