In one of the exercises, I proved that $R^n+1\subseteq R^n$ for all $n \ge1$
But now I need to give an example of relation on finite set such that $R^3 \subsetneq R^2 $
Here $R^3$ =$R \circ R \circ R$ and similarly $R^2 = R \circ R$ i.e. composition
So can anyone give an of a relation $R$ on a finite set such that $R^3 \subsetneq R^2 $. given that $R$ is transitive.