X=\{1,2,3,4\},  R,S  \subset X \times  X  , R,S are relations, we define  R \bullet S \text{ to be the set:} (x,y) \in X \times X , \text{s.t there exsits one and only one}   z \in X : (x,z) \in S,(z,y) \in R

Does this turn the set  X into a monoid?
I mean is  (R \bullet S) \bullet T =R \bullet (S \bullet T ) ?

I know the general compostion of relations is associative, but not sure about this one. any one can help?