R (A, B, C, D, E, F, G)
D → G, B
E → A
B → G, E, C
A → F, C
SALES(Cost, Emp_Name, Emp_ID , Make, Grade , Price, Serial_No, Commission, Store _Address, Date, Store _Phone, Model)
Store_Address → Store_Phone
Grade → Commission
Emp_ID → Store _Address
Serial_No → Model, Make
Emp_ID , Serial_No →Date, Cost
Emp_ID → Grade
Emp_ID → Emp_Name
The following transitive dependencies exist in the relation;
Store_Address → Store_Phone
Grade → Commission
Serial_No → Model, Make, Price
Emp_ID → Grade, Emp_Name, Store_Address
The relation is not in BCNF because the candidate key which is (Emp_ID, Serial-NO) should exist
On the left side of all the FDs which is not the case thus the relation is not in BCNF.
Decomposing sales to BCNF/3NF
This can be achieved by eliminating transitive dependencies;
Employee (Emp_ID, Grade, Emp_Name, Store_Address)
Primary key (Emp_ID)
Foreign key (Grade) references Grade (Grade)
Foreign key (Store_address) references store (store_Address)
Store (Store_Address, Store_Phone)
Grade (Grade, Commission)
Product (Serial_NO, Model, Make, Price)
Sale (Emp_ID, serial_NO, Date, Cost)
Primary key (Emp_ID, serial_NO)
Foreign key (Emp_ID) references Employee (Emp_ID)
Foreign key (Serial_No) references Product (Serial_NO)
This FD should be mapped to the Store relation to form a composite primary key.
Store (store_phone, store_address)
Primary key ( Store_Phone, Store_Address)
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