Question

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

• A. An equivalence relation
• B. Reflexive and symmetric only
• C. Reflexive and transitive only
• D. Reflexive only

Answer 1

The correct option is C

Reflexive and transitive only

Explanation for the correct option:

Checking the relation

$A=\left\{3,6,9,12\right\}$

$R=\left\{\left(3,3\right),\left(6,6\right),\left(9,9\right),\left(12,12\right),\left(6,12\right),\left(3,9\right),\left(3,12\right),\left(3,6\right)\right\}$

For all $a\in A\left(a,a\right)\in R$

$R$is reflexive

$\left(6,12\right)\in R$but$\left(12,6\right)\notin R$

Therefore $R$is not symmetric

checking transitivity:

for any $\left(a,b\right)\in R\left(b,c\right)\in R$

$(a,c)\in R$

Therefore $R$ is transitive

Hence, option (C) is the correct answer