Question

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

• A. Reflexive and transitive
• B. Reflexive and symmetric
• C. Symmetric and transitive
• D. only transitive

Answer 1

Answer: (B)

$a\in R\Rightarrow aRa\Rightarrow R$ is a reflexive relation. $\left(a , b\right)\in R\Leftrightarrow \left(b , a\right)\in R\Rightarrow R$ is symmetric a relation.
$\left(2 , 3\right)\in R,\left(3 , 5\right)\in R$ but $\left(2 , 5\right)\notin R\Rightarrow R$ is not a transitive relation.