Question

Relation $S=\left\{\right(1,2),(2,1),(2,3\left)\right\}$ is defined on the set $\{1,2,3\}$ is _________.

• A. Not transitive
• B. Symmetric
• C. Reflexive
• D. Equivalence

Answer 1

The correct option is A Not transitive

Here, as $(1,2)$ and $(2,3)$ lie in $S$, but $(1,3)$ does not lie in $S$, it is not transitive.

Also, as $(2,3)$ lies in $S$ but $(3,2)$ does not so, not symmetric.

Also, as $(1,1)$ doe not lie in $S$, it is not reflexive.

The set cannot be equivalence as it is neither symmetric nor transitive nor reflexive.