List the Armstrong's axioms for functional dependencies.  What do you understand by soundness and completeness of these axioms?    

 Ans: The Armstrong's axioms are:

• F1: Relexivity: If X is a set of attributes and Y ⊆ X afterwards X →Y holds.
• F2: Augmentation: If X → Y holds and Z is a set of attributes afterwards XZ →YZ.
• F3: Transitivity: {X → Y, Y → Z} |= {X→Z}

Soundness: By sound, we mean that a specified set of functional dependencies F specified on a relation schema R, any dependency which we can infer from F by using F1 by F3 holds in each relation state r of R that satisfies the dependencies in F.

Completeness: By complete, we mean that by using F1 through F3 frequently to infer dependencies until no more dependencies can be inferred results in the whole set of all possible dependencies which can be inferred from F.