Consider the relation schema R = (A, B, C, D, E) and the set F of functional dependencies:

A --> BC

CD --> E

B --> D

E --> A

(a) Suppose schema R is decomposed into R1 = (A, B, C) and R2 = (A, D, E). Is this decomposition a lossless-join decomposition? Why? Is this decomposition a dependency preserving decomposition? Why?

(b) Suppose schema R is decomposed into R1 = (A, B, C) and R2 = (C, D, E). Is this decomposition a lossless-join decomposition? Why? Is this decomposition a dependency preserving decomposition? Why?

(c) Find all the candidate keys for R.

(d) Using the above functional dependencies, compute the canonical cover Fc.

(e) List the three design goals for relational databases, and explain why each is desirable.

(f) Decompose schema R into BCNF.

(g) Decompose schema R into 3NF.

(h) In designing a relational database, why might we choose a non-BCNF design?