Question

Let $A=\{1,2,3,4\}$ and $R$ be a relation in $A$ given by $R=\left\{\right(1,1),(2,2),(3,3),(4,4),(1,2),(3,1),(1,3\left)\right\}$,then $R$ is:

• A. Reflexive and Transitive only
• B. Transitive and Symmetric only
• C. Equivalence
• D. Reflexive only

Answer 1

Answer: (D)

Reflexive only

The relation is reflexive as $(1,1),(2,2),(3,3)$ and $(4,4)$ exist.
It is not symmetric as $(1,2)$ exists but $(2,1)$ does not exist.
It is not transitive because $(3,1),(1,2)$ exist but $(3,2)$ does not exist.
Hence, option D is correct