Question

If a relation R on the set $\{1,2,3\}$ be defined by $R=\left\{\right(1,2\left)\right\},$ then R is

• A. transitive
• B. reflexive
• C. symmetric
• D. None of these

Answer 1

The correct option is A transitive

Check reflexivity

Given: $R=\left\{\right(1,2,\left)\right\}$ and $A=\left\{\right(1,2,3\left)\right\}$

For reflexive relation $aRa,\forall a\in A$

Here $(1,1)\notin R,$ so it is not reflexive

Check symmetricity

For symmetric relation

If $aRb\Rightarrow bRa,\forall a,b\in A$

Here $(1,2)\in R\text{but}(2,1)\notin R,$ so it is not symmetric.

Check transitivity
For transitive relation

If $aRb$ and $bRc\Rightarrow aRc\forall a,b,c\in A$

But here only one ordered pair is present.

So, we can directly conclude that $R$ is transitive
Hence, option (B) is correct one.