Question

Let $R$ be a reflexive relation on a set $A$ and $I$ be the identity relation on $A$. Then:

• A. $R\subset I$
• B. $I\subset R$
• C. $R=1$
• D. None of these

Answer 1

The correct option is B

$I\subset R$

Explanation For The Correct Option:

Determining the difference between reflexive and identity relation

Considering a set $A=\left\{1,2,3\right\}$

Now defining a relation $aRb\Rightarrow a\le b$

Therefore, $R=\left\{(1,1),(1,2),(1,3),(2,2),(2,3),(3,3)\right\}$

Since $(1,1),(2,2)\&(3,3)\in R$

Therefore, $R$ is reflexive.

We know an identity relation on a set '$A$' is the set of ordered pairs $(a,a)$, where $a\in A$

$\therefore I=\left\{(1,1),(2,2),(3,3)\right\}$

Thus, we can see that $I$ is contained in $R$.

Therefore, $I\subset R$

Hence, the correct answer is option (B)