Hmmm...I am thinking that a) is not true. Obviously R and S will agree on any point (a,b) in the intersection of R and S, but to be transitive we need another point (b,?). I see no reason why this point needs to belong to the intersection. Specifically we may have: "a R b and b R c thus a R c", but have "a S b and b S d thus a S d" where (b,c) and (b,d) do not belong to the intersection.Originally Posted by PhilipJ
Now if there are no points (b,?) in the intersection, then R and S may be transitive "vacuously" or something, so it may still work. Someone please check me on this!