What is functional dependency in the context of database normalization?

Functional dependency in the context of database normalization refers to a relationship between two sets of attributes within a database table. It describes the dependency of one set of attributes on another set of attributes. In other words, it determines how the values of one or more attributes in a table uniquely determine the values of other attributes.

A functional dependency is denoted as X -> Y, where X and Y are sets of attributes. This notation indicates that the values of attributes in set X determine the values of attributes in set Y. It means that for any two rows in the table, if the values of attributes in set X are the same, then the values of attributes in set Y must also be the same.

Functional dependencies play a crucial role in database normalization as they help in identifying and eliminating data redundancy and anomalies. By analyzing the functional dependencies, we can determine the appropriate table structure and ensure data integrity.

There are different types of functional dependencies:

1. Trivial Functional Dependency: A functional dependency is considered trivial if the set of attributes in Y is a subset of the set of attributes in X. For example, if X = {A, B} and Y = {A}, then A -> A is a trivial functional dependency.

2. Non-Trivial Functional Dependency: A functional dependency is non-trivial if the set of attributes in Y is not a subset of the set of attributes in X. For example, if X = {A, B} and Y = {C}, then A -> C is a non-trivial functional dependency.

3. Full Functional Dependency: A functional dependency is full if removing any attribute from X would break the dependency. In other words, all attributes in X are necessary to determine the values of attributes in Y.

4. Partial Functional Dependency: A functional dependency is partial if removing some attributes from X would still maintain the dependency. In this case, some attributes in X are not necessary to determine the values of attributes in Y.

Functional dependencies are used to identify and eliminate data anomalies such as insertion, deletion, and update anomalies. By decomposing a table into multiple smaller tables based on functional dependencies, we can achieve higher levels of normalization, reducing data redundancy and improving data integrity.

Overall, functional dependencies are a fundamental concept in database normalization, helping to ensure efficient and well-structured databases.