Question

The relation $R=\left\{\right(1,1),(2,2),(3,3),(1,2),(2,3),(1,3\left)\right\}$ on the set $A=\{1,2,3\}$ 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

We have $A=\{1,2,3\}$ and $R=\left\{\right(1,1),(2,2),(3,3),(1,2),(2,3),(1,3\left)\right\}$.

Since $(1,1),(2,2),(3,3)\in R$, $R$ is reflexive

R is not symmetric because $(1,2)\in R$ and $(2,1)\text{/}\in R$.

R is transitive because $(1,2),(2,3)\in R$ and $(1,3)\in R$.

$\therefore$ The correct answer is $A$.