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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 âŠ† X, then X â†’ Y

2. Augmentation: If X â†’ Y , then XZ â†’ Y Z

3. Transitivity: If X â†’ Y and Y â†’ Z, then X â†’ Z

4. Union: If X â†’ Y and X â†’ Z, then X â†’ Y Z

5. Decomposition: If X â†’ Y Z, then X â†’ Y and X â†’ Z

6. Pseudotransitivity: If X â†’ Y and W Y â†’ Z, then W X â†’ Z

7. Composition: If X â†’ Y and Z â†’ W, then XZ â†’ Y W

And find the minimal cover,

we can get

A-->BC, D-->AE

**So F and F' are same.**