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Consider the following set F of functional dependencies on the relation schema r

ID: 3634091 • Letter: C

Question

Consider the following set F of functional dependencies on the relation schema r (A, B, C,D, E, F)
A --> BCD
BC --> DE
B --> D
D --> A

Part (1)
Compute B+
Part (2)
Compute a canonical cover for the above set of functional dependencies F
Part (3)
Give a 3NF decomposition of r based on the canonical cover
Part (4)
Give a BCNF decomposition of r using original set of functional dependencies.
Part (5)
Can you get the same BCNF decomposition of r as above, using the canonical cover?

Explanation / Answer

Dear... B+ denotes the closure of B. From the set of functional dependencies, and meaning of appending a plus sign to something, however that "something". In the context of functional dependencies and normalization theory, B+, where B is one of the attributes, and meaningless by any convention . If S has a given set of FDs {A->BCD D->A ...}, then S+ is another set of FDs, which includes ALL FDs that can possibly be derived from the given set, augmented with all trivial dependencies such as A->A. For example, from A->BCD and A->A, we can infer A->ABCD. From D->A and A->BCD we can infer D->BCD. Those inferred FDs are member of S+, but not of S. B+ denotes closure of B. B --> D B+ = {BD} D --> A B+ = {ABD} A --> BCD B+ = {ABCD} BC --> DE B+ = {ABCDE} All the attributes of the relation can be found by B. So, B is the primary key of the relation.