FUNCTIONAL DEPENDENCIES & ARMSTRONG'S AXIOMS

Redundancy in relation may cause insertion, deletion and updation anomalies

Normalization is the process of minimizing redundancy from a relation or set of relations .

It helps to minimize the redundancy in relations , hence avoids anomalies .

A functional dependency (FD) for relation R is a formula of the form Aà B where A and B are sets of attributes of R.We say A functionally determines the B, or  B  is functionally dependent on the A.

Trivial functional dependency : A → B has trivial functional dependency if B is a subset of A.

Non Trivial Functional Dependency :If a functional dependency X->Y holds , where Y is not a subset of X then this dependency is called non trivial Functional dependency .

Multi valued dependency : occurs when two attributes in a table are independent of each other but, both depend on a third attribute.

Transitive dependency:  functional dependency is said to be transitive if it is indirectly formed by two functional dependencies.

 For e.g. X -> Z is a transitive dependency if the following functional dependencies hold true:                                    X->Y and Y-->Z

Armstrong's Axioms is a set of rules

It is used to infer all the functional dependencies on a relational database.

Reflexive Rule (IR1)

Augmentation Rule (IR2)

Transitive Rule (IR3)

Union/Additive  Rule (IR4)

Decomposition/Projective Rule (IR5)

Pseudo transitive Rule (IR6)