Question

Let A = {0, 1, 2, 3} and R be a relation on A defined as
R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}
Is R reflexive? symmetric? transitive?

Answer 1

We have,
R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}

$$\begin{gathered} \mathrm{As},\left(a,a\right)\in R\forall a\in A \\ \mathrm{So},R\mathrm{is}\mathrm{a}\mathrm{reflexive}\mathrm{relation} \\ \mathrm{Also},\left(a,b\right)\in R\mathrm{and}\left(b,a\right)\in R \\ \mathrm{So},R\mathrm{is}\mathrm{a}\mathrm{symmetric}\mathrm{relation}\mathrm{as}\mathrm{well} \\ \mathrm{And},\left(0,1\right)\in R\mathrm{but}\left(1,2\right)\notin R\mathrm{and}\left(2,3\right)\notin R \\ \mathrm{So},R\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{transitive}\mathrm{relation} \end{gathered}$$