Question

Let A = {1, 2, 3} and B = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is
(a) neither reflexive nor transitive
(b) neither symmetric nor transitive
(c) transitive
(d) none of these

Answer 1

(c) transitive

$$\begin{gathered} \mathrm{Reflexivity}:\mathrm{Since}(1,1)\notin B,B\mathrm{is}\mathrm{not}\mathrm{reflexive}\mathrm{on}A. \\ \mathrm{Symmetry}:\mathrm{Since}\left(1,2\right)\in B\mathrm{but}\left(2,1\right)\notin B,B\mathrm{is}\mathrm{not}\mathrm{symmetric}\mathrm{on}A. \\ \mathrm{Transitivity}:\mathrm{Since}\left(1,2\right)\in B,\left(2,3\right)\in B\mathrm{and}\left(1,3\right)\in B,B\mathrm{is}\mathrm{transitive}\mathrm{on}A. \end{gathered}$$