Question

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

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

Answer 1

Answer: (D)

Since, $\left(3,3\right),\left(6,6\right),\left(9,9\right),\left(12,12\right)\in R\Rightarrow R$ is reflexive relation.
Now $\left(6,12\right)\in R$ but $\left(12,6\right)\notin R,$ so it is not a symmetric relation.
Also $\left(3,3\right),\left(6,12\right)\in R\Rightarrow \left(3,12\right)\in R$
$\Rightarrow R$ is transitive relation.
Note : Any relation is said to be an equivalence relation, if it is reflexive, symmetric and transitive relation simultaneously.