The composition of such two constraints is the constraint  that is satisfied by every evaluation of the two non-shared variables for which there exists a value of the shared variable  such that the evaluation of these three variables satisfies the two original constraints  and .
The union of such two constraints is the constraint that is met by every assessment of the two distinct variables for which there exists a value of the common variable so that the evaluation of these three variables fulfills the two initial constraints and , indicating a shared aspect or relationship between the constraints.