Question

Let $R=\left\{(3,3)(6,6)(9,9)(12,12)(6,12)(3,9)(3,12)(3,6)\right\}$ be a relation on the set $A=\{3,6,9,12\}$. The relation is

• A. reflexive only
• B. reflexive and transitive only
• C. reflexive and symmetric only
• D. an equivalence relation

Answer 1

The correct option is B reflexive and transitive only

Given $A=\{3,6,9,12\}$
$R=\left\{(3,3)(6,6)(9,9)(12,12)(6,12)(3,9)(3,12)(3,6)\right\}$ is a relation on set $A.$
$R$ is reflexive on set $A$ as every element of set $A$ is related with itself.
$R$ is not symmetric as $(3,9)\in R$ but $(9,3)\notin R$
$R$ is transitive as $(3,6),(6,12)\in R$ .Also, $(3,12)\in R$