Third Normal Form[TNF]

Third Normal Form:[TNF]

             Let R is a relation schema X be a sub set of attribute of R and A be a attribute of R. R is TNF.

If following every functional dependency X ->A that holds over R.

One of the following statements is tree.

i)                    A -> X it is a trivial functional dependency.

ii)                   X is a super key R.

iii)                 A is part of some key of R.

           The definition of TNF is similar to that of BCNF only difference being 3^rd condition.

           To understand the 3^rd condition recall that a key for relation is a minimum set of attribute that uniquely determine another attribute. “A” must be a part of a key suppose dependency X -> A case is a validation of cause.

      There are two cause,

1.       X is a proper subset of some key K such a dependency is some time call a partial dependency.

2.       X is a not   proper subset of any key such a dependency.

Partial Dependency:

Transitive Dependency:

The set X of attribute may (or) may not has some attribute in common with key. However some redundancy is possible within 3^rd normal form. The problem associated with partial and transitive dependency persists. If there is a non drivel redundancy X -> A and “X” is Third Normal Form  because “A” is a part of Key.

Example:

Banker-info-schema = {Branch Name, Customer Name, Banker Name, Office number}

Functional dependency of R.

Banker-Name -> Branch Name, Office Number.

Customer-Name, Branch-name -> Banker Name.