/    /  DBMS – Functional Dependency (FD)

Functional Dependency (FD)

 

The existing relationship between two attributes is known as Functional Dependency.

 

Determinant: The left-hand side of functional dependency.

 

Dependent: The right-hand side of the functional dependency 

 

Let α, β be sets of attributes.

 

Definition: Consider a relation schema r(R). Let α  Í  R  and β  Í  R.

Given an instance of r(R), the instance satisfies the ‘functional dependency’ α à β, if for all pairs of tuples t1 and t2 in the instance such that  t1[α] = t2[α], it is also the case that t1[β] = t2[β].

 

 Example-1 : 

 Consider the following relation :

ABCD
a1b1c1d1
a1b2c1d2
a2b2c2d2
a2b3c2d3
a3b3c2d4

 

  

 Here, some of the possible functional dependencies (FDs) are :

A→ CD→BAB→ CCD → A
A →AB→ BC →CD →D

 

Functional Dependency is further categorised into two parts:

  • Trivial Functional dependency
  • Non-Trivial Functional dependency

 

Trivial Functional Dependency:

 

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

 

Non- Trivial Functional Dependency:

 

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

Reference Link

Functional Dependency (FD)