Functional Dependency with Examples- 

  • A Functional dependency is a relationship between attributes. Suppose that given the value of one attribute, we can obtain the value of another attribute.
  • For example, if we know the value of customer account number, we can obtain customer address, balance etc. By this, we say that
    customer address and balance is functionally dependent on customer account number.
  • In general terms, attribute Y(customer address and balance) is functionally dependent on the attribute X(customer account number), if the value of X determines the value of Y.
  • Functional dependency is represented by an arrow sign (→) that is, X→Y, where X functionally determines Y. The left-hand side attributes determine the values of attributes on the right-hand side. Attributes on the left side are called Determinants.

Let us consider a relation

Item Price(P) Number of Items(N) Total Price=P*N
100 10 1000
200 10 2000
300 10 3000
400 10 4000

Total Price = Item Price * Number of Items

In this case, Total Price is functionally dependent on Item Price and Number Of Items.

Functional Dependencies are written using the following notation:

(Item price, Number of Items) → Total Price

Consider another relation R(S#,STATUS,CITY,P#,QTY)

S# STATUS CITY P# QTY
S001 10 Ujjain P001 105
S001 10 Ujjain P002 130
S001 10 Ujjain P003 125
S001 10 Ujjain P004 200
S002 30 Surat P001 115
S002 30 Surat P002 120
S003 40 Rohtak P001 300
S004 10 Ujjain P004 400
S004 10 Ujjain P005 400

R relation hold following Functional Dependencies :

S# → CITY
S# → STATUS
CITY → STATUS
(S#,P#) → QTY

Figure 1 shows the functional dependency diagram for the relation R.

Functional Dependency Example

Properties of Functional Dependency – 

  • The Functional Dependency will deal with one to one relationship among the attributes, some times it may be one to many or many to one relationships
  • Functional Dependency must be defined on schema, not on instance of the schema. For example,
               ab  → cd
               a   → b
               ab  → c    etc.
  • A Functional Dependency must be a non trivial/semi non trivial or completely non trivial. It does not be trivial. A trivial Functional Dependency is the one where RHS is a subset of LHS.
    Example of Trivial Functional Dependency – abc  → bc
  • A Functional Dependency is non trivial if atleast one of the RHS attributes are not part of the LHS attributes.
    A Functional Dependency is completely non trivial if none of the RHS attributes are part of the LHS attributes.
    Example of Non Trivial – abc  → cde
    Example of Complete Non Trivial – abc  → def.

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