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Please answer # 4 and 5 . Problem 4 : Consider the following relation: R ( A , B , C , D , E

Please answer #4 and 5.
Problem 4: Consider the following relation:
R(A,B,C,D,E)
And the following set of functional dependencies F :
A,CE
ED
BC,E
BD
(a) Using the FDs, determine the key K of R. Hint: there is only one possible key for R.
(b) Determine a minimal basis B for F.
(c) Using K and B determined above, calculate the 3NF of this database using the synthesis
algorithm. Show the resulting relations and their keys.
Problem 5. We now want to convert R from Problem 4 to BCNF with respect to the minimal
basis B using the splitting algorithm. The algorithm would begin as follows:
S={R}
R is not in BCNF with respect to A,CE. Therefore, we split it into:
R1(A,C,D,E)
R2(B,B,C)
S={R1,R2}
Note that the key of R2 carries over from the key of the relation that was split (R).
Continue the splitting algorithm until all relations are in BCNF. Show your work. Hint: you should
need to do two more splits.
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