Question

Let $A=\{2,3,4,5\}$ be a set and $R=\left\{\right(2,2),(3,3),(4,4),(5,5),(2,3),(3,2),(5,3),(3,5\left)\right\}$ be a relation on $A$. Then $R$ is:

• A. reflexive and transitive
• B. reflexive and symmetric
• C. symmetric and transitive
• D. only transitive

Answer 1

The correct option is B reflexive and symmetric

$(a,a)\in R,\forall a\in A\Rightarrow R\text{is reflexive}$
$(a,b)\in R<=>(b,a)\in R$
$\Rightarrow R$ is symmetric
$(2,3)\in R,(3,5)\in R$
$(2,5)$ not in $R$
So, $R$ is not transitive