Question Consider the Armstrong's Axioms, where X, Y, Z and W are sets of attributes: Reflexivity: If X Y, then XY Augmentation: If X Y, then XZ YZ Transitivity: If X Y and Y Z, then X Z We can derive the following rules using Armstrong Axioms only: Union: If X Y and X Z, then X YZ Decomposition: If X YZ, then X Y and X Z Pseudo Transitivity: If X Y and WY Z, then XW Z For example, the following sequence derives Decomposition: 1. YZY (Reflexivity) 2. YZZ (Reflexivity) 3. XYZ (given in "if" part of Decomposition) 4. XY (1,3, Transitivity) 5. XZ (2,3, Transitivity) Steps 4 and 5 indicate that we have derived the FDs in the "then" part of Decomposition, so we are done. Note that each step in the above derivation is obtained from Armstrong Axioms (such as 1 and 2), or the FDs given in the "if" part of the rule to be derived (such as 3), or applying Armstrong Axioms to previously obtained FDs (such as 4 and 5). Other than these, you are not allowed to use anything else. You are asked to derive the Union rule and