Consider a relation schema R(XYZ) with functional dependencies XY->Z and Z->X. Can we conclude that Y->XZ?

Exercise 2 (Functional Dependencies and Normal Forms) [30 points]

1. [5 points] Consider a relation schema R(XYZ) with functional dependencies XY->Z and Z->X. Can we conclude that Y->XZ? If yes, please proof it. If no, please give a counter example.
2. [8 points] Given the relation schema R = (A, B, C, D, E) and the canonical cover of its set of functional dependencies Fc = { A→BC CD →E B →D E →A}. Compute a lossless join decomposition in Boyce-Codd Normal Form for R. Show your steps clearly.

3. [4 points] Is this decomposition dependency-preserving? Why or why not?
4. [6 points] Compute the Canonical Cover for F = {A →B, ABCD →E, EF →GH, ACDF →EG}. List the steps in detail.
5. [3 points] List all attribute sets from below that are candidate keys (if any) based on the above question.

AB ACDE ACDF CDG

6. [4 points] Is the answer you computed from Question 4 in 3NF? Is it in 2 NF? Why or why not?