What are functional dependencies?

Functional dependencies in the context of databases refer to relationships between attributes (or columns) in a table. A functional dependency occurs when the value of one attribute uniquely determines the value of another attribute in the same table. Formally, if for two attributes \( A \) and \( B \) in a table, every value of \( A \) is associated with exactly one value of \( B \), \( A \) is said to functionally determine \( B \), denoted as \( A \rightarrow B \).

For example, if in a table \( T \), the attribute \( A \) uniquely determines the attribute \( B \), then \( A \rightarrow B \) is a functional dependency. This means that for each value of \( A \), there is exactly one corresponding value of \( B \) in the table.

Functional dependencies are essential in database design and normalization processes to ensure data integrity and to eliminate redundancy.