Question

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

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

Answer 1

The correct option is D reflexive and transitive only

Here, $(3,3),(6,6),(9,9),(12,12)\in R\therefore$ R is reflexive.
Now, $(6,12)\in R$ but $(12,6)\notin R\therefore R$ is not symmetric.
Also, $(3,6),(6,12)\in R\Rightarrow (3,12)\in R\therefore R$ is transitive.