(A) For the relation;

CarSales (RegNo, BuyerName, Address, SalesPerson, Make, Model, Commission)

The following functional dependences hold,

RegNo _ID à Make, Model

RegNoà Commission

RegNo, BuyerName à SalesPerson

BuyerName à Address

Make, Model à Commission

RegNo à SalesPerson

a. Use Inference rules to find the minimal basis and determine the Key of the relation

b. Based on this key, determine if the relation is in BCNF.

c. If it is not in BCNF then decompose the relation into BCNF.

3(B) The following relation holds details about cars ;

CAR_DETAILS(Registration_No , Make , Model , Tow_Load , Engine_Size, Colour )

And has the following functional dependencies;

Make , Model -> Engine_Size

Registration_No -> Make, Colour, Model

Engine_Size -> Tow_Load

The relation is decomposed into ;

CAR_DETAILS1(Registration_No , Colour, Make , Engine_Size* ,Model)

CAR_DETAILS2(Engine_Size, Tow_Load)

Prove that the decomposition is incomplete and complete the decomposition.