A *functional dependency* (FD) is a relationship between two
attributes, typically between the PK and other non-key attributes within
a table. For any relation R, attribute Y is functionally dependent on
attribute X (usually the PK), if for every valid instance of X, that
value of X uniquely determines the value of Y. This relationship is indicated by the representation below :

**X ———–> Y**

The left side of the above FD diagram is called the* determinant*, and the right side is the *dependent*.

For a given relation there exit some additional FD's apart from given one. Such FD's are determined with some procedure. Consider the following example

Problem: Check all additional FD's for the relation R(AB) with FD = { A->B, B->A}

Solution:

If an FD X-->B, then in place of X we can write A,B,AB, Ð¤

Now find the closures of A,B,AB, Ð¤

A+={ A,B}; two attributes in A+ then 2^2 = 4 FD's

B+={ B,A} ; 2^2= 4 FD's

AB+ ={A,B}; 2^2 = 4

and one additional FD Ð¤ ->Ð¤

Total number of FD's are = 4+4+4+1= 13

Since two FD's are already given ( A->B, B->A), then additional FD's are = 13-2 = 11

and invalid FD's are

Ð¤ ->A

Ð¤ ->B

Ð¤ ->AB

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