Give a necessary and sufficient condition for a decomposition of R into R1 and R

Question

Give a necessary and sufficient condition for a decomposition of R into R1 and R2 to be lossless join. Very briefly explain why the condition is necessary and sufficient. a. b. Given F-A-B, A-C, CG- H, CG-I,B-H), set of functional dependencies on R(A, B, C, G, H, I), check if A is a candidate key of R. ldentify possible f used by a Toyota dealer, Car-sell (transactioniD custo MakeYear, carPrice, NoOfSeats) merlD, CustomerName, customerAddress, carModel, d. Check if the schema car-sell of (c) is in BCNF form. Explain your answer.

Explanation / Answer

a)

To check for lossless join decomposition using FD set, following conditions must hold:

1) Union of Attributes of R1 and R2 must be equal to attribute of R. Each attribute of R must be either in R1 or in R2.
Att(R1) U Att(R2) = Att(R)
2) Intersection of Attributes of R1 and R2 must not be NULL.
Att(R1) ? Att(R2) ? ?
3) Common attribute must be a key for at least one relation (R1 or R2)
Att(R1) ? Att(R2) -> Att(R1) or Att(R1) ? Att(R2) -> Att(R2)

b) yes A is a candidate key of R because it's attribute closure gives all the attributes.

c) Functional dependencies are

Customer_id -> Customer_name   
Customer_id -> Customer_address   
car_Model -> car_price   
car_Model -> Make_year   
car_Model -> no_of_seats

D) The relation is not in BCNF because the LHS of functional dependencies is not a super key.

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