hi

my teacher wants us to think a conjecture for the invertible relation and then prove it, but I have absolutely no idea how to find that conjecture. Any help is appreciated.

$\displaystyle R,S \subset X \times X $ , we define $\displaystyle R \bullet S \text{ to be the set:} (x,y) \in X \times X , \text{s.t there exsits one and only one}$ $\displaystyle z \in X : (x,z) \in S,(z,y) \in R $

like a relation $\displaystyle \mathcal{R} \subset X \times X $ is invertible with respect to $\displaystyle \bullet $ if and only if (what condition does R has to satisfy?)

any idea?

cheers.