A _________ Fc for F is a set of dependencies such that F logically implies all dependencies in Fc, and Fc logically implies all dependencies in F.a)Canonical coverb)Complete coverc)Canonical dependencyd)Canonical clauseCorrect answer is option 'A'. Can you explain this answer?

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Answer

Understanding Canonical Cover
A canonical cover is an essential concept in database theory, particularly in the context of functional dependencies. It serves to simplify a set of functional dependencies while preserving their meaning.
Definition of Canonical Cover
- A canonical cover for a set of functional dependencies $ F $ is a minimal set $ Fc $ such that:
- Logical Implication: $ F \models Fc $ (meaning every dependency in $ Fc $ is implied by $ F $).
- Equivalence: $ Fc \models F $ (meaning every dependency in $ F $ is implied by $ Fc $).
Importance of Canonical Cover
- Simplification: It reduces redundancy in the set of functional dependencies. By having a minimal set, it becomes easier to analyze and implement.
- Efficiency: Working with a canonical cover can lead to more efficient database design and normalization processes.
Characteristics of Canonical Cover
- Minimality: No functional dependency in $ Fc $ can be removed without altering the meaning of the set.
- Irreducibility: Each dependency in $ Fc $ should not be expressible as a union of other dependencies.
Conclusion
In summary, option A, 'Canonical cover,' is the correct answer because it encapsulates the properties of dependencies in a manner that maintains both logical implication and equivalence between the original set $ F $ and the reduced set $ Fc $. This makes it a vital tool in database normalization and the management of functional dependencies.

Answer

A Canonical cover Fc for F is a set of dependencies such that F logically implies all dependencies in Fc, and Fc logically implies all dependencies in F. In Fc, no functional dependency should contain an extraneous attribute and each left side of functional dependency should be unique.

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