$\text{ Let }A=\left\{A_1,A_2,A_3,A_4,A_5,A_6\right\}\text{ be the set of six unit circles with centres }{C}_1,C_2,C_3,\dots \dots ..C_6$

arranged as shown in the diagram. The relation R on A is defined by 

$\left(A_i,A_j\right)\in R\iff C_i{C}_j\le 2\sqrt{2}\text{ then }$

 

$\begin{array}{l}\left(i\right) \left(C_i,C_i\right)=0\le 2\sqrt{2},for i=\mathrm{1.2...6}\\ \Rightarrow \left(A_i,A_i\right)\in R\forall i\text{} R is reflexive\text{}\\ \left(ii\right) Let \left(A_i,A_j\right)\in R\text{} \\ \Rightarrow C_i{C}_j\le 2\sqrt{2}\text{} \\ \Rightarrow C_j{C}_i\le 2\sqrt{2}\text{} \\ \Rightarrow \left(A_j,A_i\right)\in R\text{ }\\ \Rightarrow \text{R is symmetric}\end{array}$

$$\begin{gathered} \left(iii\right) We see that \left(A_1,A_2\right)\in R,\left(A_2,A_3\right)\in R, but\left(A_1,A_3\right)\notin R. \\ \Rightarrow R is not transitive \end{gathered}$$