2. (25%) Consider the following set of funcitonal dependencies, F, over the schema R(A,B,C,D,E):

A DE

BE C

DB

C A

a) (8%) Is the decomposition of R into R1(A,B,C) and R2(A,D,E) a lossless join decomposition? Why or why not?

b)(8%) Is the decomposition listed in part a (R1(A,B,C) & R2(A,D,E)) dependency preserving? Why or why not?

c)(9%) Show that R is not in Boyce Codd Normal Form and provide a lossless join decomposition of R into Boyce Codd Normal Form