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. $\left(a,b\right)\in R\iff \left(b,a\right)\in R\Rightarrow R$ 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.