Functional Dependency (FD)

The functional dependency (FD) is a relationship that exists between two attributes, Where one attribute can directly or indirectly derived from the other attribute. Syntax:
X   →   Y  
The left side of the FD (attribute X) is known as a determinant, and the right side of the FD (attribute Y) is known as a dependent. So “Y” can determined from “X”.

Types of FD

There are two types of functional dependency
  • Trivial FD
  • Non Trivial FD

Let’s explain with an example:

Suppose we have a Student table with attributes: Student_Id, Student_Name, Student _class. Here, the Student_Id attribute can uniquely identify the Student_Name and Student_address attributes of the Student table.

1. Trivial FD

  • A → B has trivial functional dependency if B is a subset of A or B.
  • it is the case where the derived attribute is derived directly
  • The following dependencies are also trivial: A → A, B → B
Example:
  • {Student_id, Student_Name}   → Student_Id  // it is a trivial functional dependency as Student_Id is a subset of { Student_Id, Student_Name}.  
  • Also, Student_Id → Student_Id and Student_address →   Student_address are trivial dependncies   

Keep In Mind

  • The intersection of the left-hand side of FD and right-hand side of FD will never be a null
  • L.H.S ∩ R.H.S ≠ Ø
  • Travail FD is valid in each case and never be problematic in transactions

2. Non-Trivial FD

  • A → B has a non-trivial functional dependency if B is not a subset of A.
  • it is the case where the derived attributes are not derived directly
Example: As in the following example, Student_address is derived from student_ID but not directly.
  • Student_ID   →    Student_Name  
  • Student_Name   →    Student_Address  

Keep In Mind

  • When ‘A’ intersection ‘B’ is NULL, then A → B is called as complete non-trivial.
  • The intersection of both left and right side will always be null (A ∩ B = Ø)
  • Non-travial are not valid in each case