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Functional Dependency :

Let attributes X and Y are two subsets of attributes of relation R.
If the values of the X component of a tuple uniquely (or functionally) determine the values of the Y component, then, there is a functional dependency from x to Y.

Algorithm:

Input: Let F be a set of FDs for relation R.

Let f: A  B is a FD to be examined for redundancy.

Steps:

F’ = F – f
T = A
For each FD: xy in F’ Do

If X subsetT Then

T = T  Y

End if

End for

4. If B subsetT Then

f: A  B is redundant.

End if

Output: Decision whether a given FD f: A  B is redundant or not.

Once a set of FDs for any relation R is given, it may be possible that this set contains redundant FDs.
“ A FD in the set is redundant, if it can be derived from the other FDs in the set”.
This algorithm is known as membership algorithm.
A set of functional decencies F for relation R is called Minimal or Irreducible cover of asset of functional dependencies, if it does not have any redundant functional dependency.

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