Consider the relation schema R=VWXYZ, with the set of functional dependencies F={VW?XY, V?X, W?Z, YZ?Z, Z?V}. a) [3x2 marks] Give three independent reasons why the following table cannot possibly be a legal instance of R. b) Show the functional dependencies that hold on each of R1=VWX and R2=WYZ. You do not need to show trivial functional dependencies, or those implied by others in the same set, but you must show all others.

c) Is the decomposition of R into R1=VWX and R2=WYZ lossless-join? Why or why not?

d) Find a lossless-join BCNF decomposition of R (note: you cannot use the decomposition from part (c) above). At each step, you must show all FDs that hold on each of the resulting relations. You do not need to show FDs that are trivial or implied by other FDs in the same set, but you must show all others.

e) Is your decomposition found in part (d) dependency-preserving? Why or why not?

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