Question

If A = {a, b, c, d}, then a relation R = {(a, b), (b, a), (a, a)} on A is
(a) symmetric and transitive only
(b) reflexive and transitive only
(c) symmetric only
(d) transitive only

Answer 1

(a) symmetric and transitive only

$$\begin{gathered} \mathrm{Reflexivity}:\mathrm{Since}\left(b,b\right)\notin R,R\mathrm{is}\mathrm{not}\mathrm{reflexive}\mathrm{on}A. \\ \mathrm{Symmetry}:\mathrm{Since}\left(a,b\right)\in R\mathrm{and}\left(b,a\right)\in R,R\mathrm{is}\mathrm{symmetric}\mathrm{on}A. \\ \mathrm{Transitivity}:\mathrm{Since}\left(a,b\right)\in R,\left(b,a\right)\in R\mathrm{and}\left(a,a\right)\in R,R\mathrm{is}\mathrm{transitive}\mathrm{on}A. \end{gathered}$$