. Prove that these inference rules are sound. . Are these inference rules complete? If so, then prove why. Otherwise, show why not. HINT: You may assume that the Armstrong Axioms are complete. . Are these inference rules independent? If so, then show why. Otherwise, show why not. Consider the following two inference rules: 1. Y Y for all sets of attributes Y. 2. If XY, Y Z, and a B, then XB Za.