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.

 

  1. [4 points] Is this decomposition dependency-preserving? Why or why not?
  2. [6 points] Compute the Canonical Cover for F = {A →B, ABCD →E, EF →GH, ACDF →EG}. List the steps in detail.
  3. [3 points] List all attribute sets from below that are candidate keys (if any) based on the above question.

 

AB ACDE ACDF CDG

  1. [4 points] Is the answer you computed from Question 4 in 3NF? Is it in 2 NF? Why or why not?
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