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The definition in my book says:

The set of all functional dependencies logically implied by F is the closure of F.

My question is, do we include FDs in F in F closure as well ?

If I have:

  • F = {A→B, B→C}

  • a) F+ = {A→C, A→BC, A→B, B→C}

  • b) F+ = {A→C, A→BC}

Which one would be correct a) or b) ?

1 Answer 1

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Since each dependency implies itself (given the fact that in logic trivially every assertion implies itself), F is included in F+. But note that in your example F+ contains quite a large number of dependencies, in addition to the dependencies that you have listed, like for instance A→A, AB→C, B→B, AC→A, etc.

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