Question

Let $A=\{1,2,3\}$ and consider the relation $R=\{(1,1),(2,2)(3,3),(1,2),(2,3),(1,3)\}$, then $R$ is

• A. reflexive but not symmetric
• B. reflexive but not transitive
• C. symmetric and transitive
• D. neither symmetric nor transitive

Answer 1

The correct option is A reflexive but not symmetric

Relation $R$ is reflexive relation over set $A$ as every element of $A$ is related to itself in $R$.

Relation $R$ is not symmetric as $(1,2)$ is in $R$ but $(2,1)$ is not in $R$.

Relation $R$ is also transitive as for $a,b,c$ in $A$, if $(a,b)$ is in $R$ and $(b,c)$ is in $R$, then $(a,c)$ is also in $R$.

Thus $A$ is correct answer .