# Functional Dependencies/Armstrong's Axioms

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### #1 taskforce141

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# Functional Dependencies/Armstrong's Axioms

Posted 18 November 2013 - 05:46 PM

Hi,

This isn't a question relating to an actual database, but more of a database logic question on functional dependencies.

I have the relation R(A, B, C, D, E, F), and FD={AB->C, AD->B, C->B, F->AD, F->E}. I need to prove that F is a super key of R, and I need to do it through Armstrong's Axioms. I'm not very confident on whether or not I did this right, but here are my steps.

1) F -> E Given
2) F -> AD Given
3) F -> EAD 1, 2, Augmentation
4) AD -> B Given
5) F -> B 2, 4, Transitivity
6) F -> BEAD 3, 5, Augmentation
7) AB -> C Given
8) F -> C 6, 7, Transitivity (Not sure on this one, but my reasoning is that since F -> BEAD, then F -> AB -> C)
9) F -> CBEAD 6, 8, Augmentation

Therefore, F is a super key of R. Would this be the correct way of tackling this problem? Am I even headed in the right direction?

Thanks.

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