| 248 | |
| 249 | == Conclusion |
| 250 | From our Normalization process we obtained the relations who all satisfy BCNF: |
| 251 | |
| 252 | R7(StaffRole), R8(FrontStaff), R9(Customer), R10(Reservation), R3(Table) R6 (FrontStaff_Managed_reservation) - Reservation Management |
| 253 | |
| 254 | R3(Manager), R4(Shifts), R5(Employees), R6(Assigments) - Shift Managements |
| 255 | |
| 256 | R4 (Payments), R5 (Tables), R6 (Orders), R8 (OrderItems), R9 (Categories), and R10 (Products) - Order Management |
| 257 | |
| 258 | The decomposition satisfies lossless join because every decomposition step was carried out on keys, ensuring that the intersection attribute is always a key in at least one of the projections. This guarantees that recombining the smaller relations reconstructs the original relation without producing spurious tuples. |
| 259 | |
| 260 | Additionally, the decomposition is dependency preserving since all functional dependencies are still enforceable inside individual relations. No dependency spans across different relations in a way that would require reconstructing joins. Therefore, the final schema preserves both theoretical guarantees. |