Functional Dependency


What do you mean by functional dependency?

It is defined as relation among two attributes, between primary key and another non-prime attribute within any table. For any relation R, attribute B is functionally dependent on attribute A, here we can say that value of A determines value of B uniquely.

Here, A will act as determinant,
B will act as a dependent.

The relation can be indicated using -> symbol, in following manner:

A -> B

Let us take one example:
Let us consider, we have student table consisting of Roll_no, Name, Age, Bdate, Address. So here, Roll_no can determine Name, Age, Bdate, Address.

Roll_no -> Name, Age, Bdate, Address.
Rules of Functional Dependencies

1. Reflexive rule:- If A is a set of attributes and B is subset of A, then A holds the value of B.

If A ⊇ B then A → B

        A = {a, b, c, d, e}  
        B = {a, b, c}  

2. Augmentation rule:-   When A -> B holds, and c is attribute set, then ac -> bc also holds. Thus we can add attributes which do not change the basic dependencies.

If A -> B, then AC -> BC

For a relation R(ABCD), if A -> B then AC -> BC

3.Transitive rule:-  If A determines B and B determines Z, then A determines Z.

If  A -> B and B -> C holds, then A ->C holds.

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