Question

Is the relation $R$ defined on a set $A=\{a,b,c\}$ as follows:
$R=\{(a,a),(a,b),(a,c),(b,b),(b,c),(c,a),(c,b),(c,c)\}$ is (i) reflexive (ii) symmetric (iii) transitive

Answer 1

Given the relations on the set $A$ is

i$R=\{(a,a),(a,b),(a,c),(b,b),(b,c),(c,a),(c,b),(c,c)\}$

This relation is reflexive as for all $a\in A$, $(a,a)\in R_1$.

As $(a,b)\in R$ but $(b,a)\notin R$ so $R$ not symmetric.

Now $(b,c)\in R,(c,a)\in R$ but $(b,a)\notin R$, so the relation is not transitive.