1. Use the definition of functional dependency to argue that each of Armstrong’s axioms (reflexivity, augmentation, and transitivity) is sound. 2. Consider the following proposed rule for functional...

1. Use the definition of functional dependency to argue that each of Armstrong’s axioms (reflexivity, augmentation, and transitivity) is sound.

2. Consider the following proposed rule for functional dependencies: If α → β and γ → β, then α → γ. Prove that this rule is not sound by showing a relation r that satisfies α → β and γ → β, but does not satisfy α → γ.