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Closure of a set of Functional Dependencies

Let F be a set of Functional Dependencies on R.

Let f is not a part of F.

And, let f is applicable on r(R).

Then, f is said to be ‘logically implied’ by f.

 

Example-1:   

 

Let S = (A, B, C, G, H, I)

F =  [ A → B, A → C, CG → H, CG → I, B → H ]

Here, the FD:  A → H  is said to be ‘logically implied’ FD.

Similarly, AG → I is also ‘logically implied‘ FD.

These two FDs are not in F but in F +.

And the set of FDs F is also part of F +.

Hence, the set F + contains two types of FDs. One is the set F, and the other is the set of logically implied FDs of F. This F + is known as ‘Closure of F’.

 

Reference Link

Closure of a set of Functional Dependencies