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What are set of FDs for the relation in DBMS?

Asked on January 03, 2015
Consider the following set of FDs for the relation R(A, B, C, D, E):
F= {A-->B, AB-->C, D-->AC, D-->E}
F'= {A-->BC, D-->AE}
Check whether these are equivalent sets.

Replied on January 04, 2015
A-->B means A functionally defines B.
AB-->C means A and B functionally defines  C
D--> AC means D functionally defines A and C
D--> E means D functionally defines E

If understand the properties of functional dependency as given below

1. Reflexivity: If Y ⊆ X, then X → Y
2. Augmentation: If X → Y , then XZ → Y Z
3. Transitivity: If X → Y and Y → Z, then X → Z
4. Union: If X → Y and X → Z, then X → Y Z
5. Decomposition: If X → Y Z, then X → Y and X → Z
6. Pseudotransitivity: If X → Y and W Y → Z, then W X → Z
7. Composition: If X → Y and Z → W, then XZ → Y W 

And find the minimal cover,

we can get 

A-->BC, D-->AE

So F and F' are same.

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