Question $3$

Let $A=\{1,2,3\}$ and $R$ and $S$ be two relations defined on $A$ as follows:

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

$S=\{(1,1),(2,2),(1,3),(2,1),(3,1),(1,2)\}$

Which of the following statements are correct?

I. $R$ is transitive but $S$ is not transitive.

II$.R$ is not symmetric but $S$ is symmetric.

III. Neither $R$ nor $S$ is antisymmetric.

IV$.R$ U $S$ is reflexive.

V$.$ S $-R$ is antisymmetric.

a$.$ IV and $V$

b$.$I and III

c$.$ II$,$ III, IV and V

d$.$ II$,$ II$,$ III, IV and V