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