Functional Dependency

The functional dependency is a relationship that exists between two attributes. It typically exists between the primary key and non-key attribute within a table.

X   →   Y  

The left side of FD is known as a determinant, the right side of the production is known as a dependent.

For example:

Assume we have an employee table with attributes: Emp_Id, Emp_Name, Emp_Address.

Here Emp_Id attribute can uniquely identify the Emp_Name attribute of employee table because if we know the Emp_Id, we can tell that employee name associated with it.

Functional dependency can be written as:

Emp_Id → Emp_Name   

We can say that Emp_Name is functionally dependent on Emp_Id.

Types of Functional dependency

1. Trivial functional dependency

• A → B has trivial functional dependency if B is a subset of A.
• The following dependencies are also trivial like: A → A, B → B

Example:

Consider a table with two columns Employee_Id and Employee_Name.  
{Employee_id, Employee_Name}   →    Employee_Id is a trivial functional dependency as   
Employee_Id is a subset of {Employee_Id, Employee_Name}.  
Also, Employee_Id → Employee_Id and Employee_Name   →    Employee_Name are trivial dependencies too.  

2. Non-trivial functional dependency

• A → B has a non-trivial functional dependency if B is not a subset of A.
• When A intersection B is NULL, then A → B is called as complete non-trivial.

Example:

ID   →    Name,  
Name   →    DOB