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Functional dependency is a relationship that exists when one attribute uniquely determines another attribute.
If R is a relation with attributes X and Y, a functional dependency between the attributes is represented as X->Y, which specifies Y is functionally dependent on X. Here X is a determinant set and Y is a dependent attribute. Each value of X is associated with precisely one Y value.
Functional dependency in a database serves as a constraint between two sets of attributes. Defining functional dependency is an important part of relational database design and contributes to aspect normalization.
Techopedia Explains Functional Dependency
A functional dependency is trivial if Y is a subset of X. In a table with the attributes of employee name and Social Security number (SSN), employee name is functionally dependent on SSN because the SSN is unique for individual names. An SSN identifies the employee specifically, but an employee name cannot distinguish the SSN because more than one employee could have the same name.
Functional dependency defines Boyce-Codd normal form and third normal form. This preserves dependency between attributes, eliminating the repetition of information. Functional dependency is related to a candidate key, which uniquely identifies a tuple and determines the value of all other attributes in the relation. In some cases, functionally dependent sets are irreducible if:
- The right-hand set of functional dependency holds only one attribute
- The left-hand set of functional dependency cannot be reduced, since this may change the entire content of the set
- Reducing any of the existing functional dependency might change the content of the set
An important property of a functional dependency is Armstrong’s axiom, which is used in database normalization. In a relation, R, with three attributes (X, Y, Z) Armstrong’s axiom holds true if the following conditions are satisfied:
- Axiom of Transivity: If X->Y and Y->Z, then X->Z
- Axiom of Reflexivity (Subset Property): If Y is a subset of X, then X->Y
- Axiom of Augmentation: If X->Y, then XZ->YZ
