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’.
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