What are the properties of Functional dependencies in canonical cover

What are the properties of canonical cover in DBMS? List down the properties that are to be held by set of FDs in a minimal cover, Discuss about the properties of canonical cover 

Properties of functional dependencies in canonical cover (minimal cover)

Canonical cover of a set of functional dependencies F is mentioned as F_c.

A canonical cover F_c of a set of functional dependencies F has the following properties;

1. Canonical cover F_c is equivalent to F.

F logically implies all dependencies in F_c and F_c logically implies all dependencies in F. 

2. Any functional dependency in F_c cannot be redundant. F_c is minimal set of FDs.

If we remove any functional dependency from F_c, then F_c will no longer be equivalent to F. Removal of any FD from F_c eliminates property 1.

3. The functional dependencies in F_c do not contain redundant attributes on either side.

If X is a set of attributes and Y is another set of attributes, then X → Y is a functional dependency. If X → Y is part of F_c, then removal of any attributes on either side of the functional dependency X → Y result in loss of equivalency between F_c and F.

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