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. $I\subseteq R$
• C. $R\subseteq I$
• D. $I\subset R$

Answer 1

The correct option is B $I\subseteq R$

We know that an Identity relation is always subset of reflexive relation i.e.,$I\subseteq R$
Consider an example,
$A=\{1,2,3\}$
$I=\left\{\right(1,1),(2,2),(3,3\left)\right\}$
$R=\left\{\right(1,1),(2,2),(3,3),(1,2),(2,3\left)\right\}$
$\therefore I$ is always a subset of $R$