Functional Dependency

A Functional Dependency is a relationship or constraint between two attributes or two sets of attributes in a relation. It is the core theoretical concept that guides the process of database normalization. A functional dependency is denoted by an arrow, X → Y, where X and Y are sets of attributes. This expression is read as 'X functionally determines Y' or 'Y is functionally dependent on X'. It means that for any valid instance of the relation, the value of X uniquely determines the value of Y. In other words, if two tuples (rows) have the same value for X, they must also have the same value for Y. For example, in a `Students` table with attributes `student_id` and `student_name`, there is a functional dependency `student_id` → `student_name`. This is because for any given `student_id`, there can only be one corresponding `student_name`. The left side of the arrow is called the 'determinant', and the right side is the 'dependent'. By identifying all the functional dependencies in a set of data, a database designer can determine the appropriate way to group attributes into tables and identify candidate keys (if X → all other attributes, then X is a superkey). Normalization is essentially the process of analyzing these dependencies and restructuring tables to eliminate undesirable ones, such as partial dependencies (for 2NF) and transitive dependencies (for 3NF).