Let A=A1,A2,A3,A4,A5,A6 be the set of six unit circles with centres C1,C2,C3,……..C6arranged as shown in the diagram. The relation R on A is defined by Ai,Aj∈R⇔CiCj≤22 then

i Ci,Ci=0≤22,for i=1.2...6      ⇒ Ai,Ai∈R∀i​      R is reflexive​ii Let Ai,Aj∈R​            ⇒CiCj≤22​            ⇒CjCi≤22​            ⇒Aj,Ai∈R​      ⇒R is symmetric(iii) We see that A1,A2∈R,A2,A3∈R, butA1,A3∉R.        ⇒R is not transitive