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.