Question

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

• A. symmetric
• B. transitive
• C. reflexive
• D. anti-symmetric

Answer 1

The correct option is A symmetric

if $xRx$ is reflexive then $(1,1),(2,2),(3,3)\Rightarrow R$

but $(3,3)$ is missing.

similarly for transitive if $(1,2),(1,3)\Rightarrow (2,3)$, but $(2,3)$ is missing.

now for symmetric $(1,2),(2,1),(1,3),(3,1)$ all elements are here

hence,answer is Option $A$ symmetric.