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How to find minimum cover for any set in DBMS?



Asked on January 03, 2015
A set of FDs for the relation R(A, B, C, D, E, F) is AB-->C, C-->A, BC-->D, ACD--> B, BE-->C, EC-->FA, CF-->BD, D-->E. Find a minimum cover for this set.


Replied on January 04, 2015
1. AB--> C
2. C -->A
3. BC-->D
4. ACD-->B
5. BE-->C
6. EC-->FA
7. CF-->BD
8. D-->E

To apply the minimal cover we need to follow the below steps.

1. Remove all trivial functional dependencies
2. Repeatedly apply until no changes are possible
3. Union Simplification 
4. RHS Simplification
5. LHS Simplification

If we minimize, we may get
1. AB--> C
2. C -->A
3. BC-->D
4. CD-->B
5. BE-->C
6. EC-->F
7. CF-->BD
8. D-->E








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