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

Answer: (C)

reflexive only

$1)A=\{3,6,9,12\}$ and $(3,3),(6,6),(9,9),(12,12)\in R\Rightarrow R$ is reflexive
$2\left)\right(6,12)\in R$ but $(12,6)\notin R\Rightarrow R$ is not symmetric
$3\left)\right(3,6)\in R,(6,1)\notin R\Rightarrow (3,12)\in R$
$\therefore R$ is not transitive