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: (D)

reflexive and transitive only

In some cases if $(a,b)\in R$ ,$(b,a)\notin R$

$\therefore$ relation is not symmetric which means our choice (a)

and (b) are out of court. We needed to reflexivity and transitivity.

For reflexivity $a\in R,(a,a)\in R$ which is hold $i.e.$ $R$ is reflexive .

Again,

for transitivity if $(a,b)\in R,(b,c)\in R\Rightarrow (a,c)\in R$

which is also true in $R=\left\{\right(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6\left)\right\}$