Question

Let R be a relation such that $R=\{(1,4),(3,7),(4,5),(4,6),(7,6)\}$ then ${\left(R^{-1}oR\right)}^{-1}=$

• A. $\{(1,1),(3,3),(4,4),(7,7),(4,7),(7,4),(4,3)\}$
• B. $\{(1,1),(3,3),(4,4),(7,7),(4,7),(7,4)\}$
• C. $\{(1,1),(3,3),(4,4)\}$
• D. $\varphi$

Answer 1

The correct option is D $\varphi$

$R=\{(1,4),(3,7),(4,5),(4,6),(7,6)\}$

We observe that the function is onto but not one-one

We know that inverse exists only for bijective functions

$\therefore R^{-1}$ doesn't exist.