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.