Question

The relation $R=\{(1$, $1)$, $(2$, $2)(3$, $3)$, $(1$, $2)$, $(2$, $3)$, $(1$, $3)\}$ on 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

Answer: (A)

Reflexive : $(1$, $1)$, $(2$, $2)$, $(3$, $3)\in R$, $R$ is reflexive
Symmetric : $(1$, $2)\in R$ but $(2$, $1)\notin R$, $R$ is not symmetric.
Transitive : $(1$, $2)\in R$ and $(2$, $3)\in R$
$\Rightarrow (1$, $3)\in R$, $R$ is transitive.