## Transitive closures

Hi,

I'm trying to find this example since 4 hours, but can't find one. I'm starting thinking it's impossible...

Find an example of relations $R_1$ and $R_2$ on some set $A$ such that, if we let $R = R_1 \setminus R_2$ and we let $S_1$, $S_2$ and $S$ be the transitive closures of $R_1$, $R_2$ and $R$ respectively, then $S_1 \setminus S_2 \not\subseteq S$ and $S \not\subseteq S_1 \setminus S_2$.