Question

What do you mean by reflexive transitive and symmetric relation? Explain with some suitable examples.

Answer 1

Define reflexive transitive and symmetric relation.

Reflexive Relation: A relation $R$ on a set $A$ is called reflexive if$(a,a)\in R$ holds for every element $a\in A$

.i.e. if $\mathrm{set}A=\{a,b\}$ then $R=\{(a,a),(b,b)\}$ is reflexive relation.

Transitive Relation: A relation $R$ on a set $A$ is called transitive if $(a,b)\in R$ and $(b,c)\in R$ then $(a,c)\in R$ for all $a,b,c\in A$

.i.e. Relation $R=\left\{\right(1,2),(2,3),(1,3\left)\right\}$ on $\mathrm{set}A=\{1,2,3\}$ is transitive.

Symmetric Relation: A relation $R$ on a set $A$ is called symmetric if $(b,a)\in R$ holds when$(a,b)\in R$

i.e. The relation $R=\left\{(4,5),(5,4),(6,5),(5,6)\right\}$ on $\mathrm{set}A=\{4,5,6\}$ is symmetric.