Armstrong axioms


#1

How can we prove the soundness of the Union rule via Armstrong’s Axioms


#2

Union: if X → Y and X → Z then X → Y Z.

Proof: Using Armstrong’s Axioms:

  1. X → Y , Given
  2. X → Z, Given
  3. X → XZ, Augment 2 by X
  4. XZ → Y Z, Augment 1 by Z
  5. X → Y Z, Transitivity using 3 and 4.