Question

Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R is
(a) identify relation
(b) reflexive
(c) symmetric
(d) antisymmetric

Answer 1

(b) reflexive

$$\begin{gathered} \mathrm{Reflexivity}:\mathrm{Since}\left(a,a\right)\in R\forall a\in A,R\mathrm{is}\mathrm{reflexive}\mathrm{on}A. \\ \mathrm{Symmetry}:\mathrm{Since}\left(a,b\right)\in R\mathrm{but}\left(b,a\right)\notin R,R\mathrm{is}\mathrm{not}\mathrm{symmetric}\mathrm{on}A. \\ \Rightarrow R\mathrm{is}\mathrm{not}\mathrm{antisymmetric}\mathrm{on}A. \\ \mathrm{Also},R\mathrm{is}\mathrm{not}\mathrm{an}\mathrm{identity}\mathrm{relation}\mathrm{on}A. \end{gathered}$$