Show that the following decomposition of the schema R of Practice Exercise 8.1 is not a lossless decomposition:
(A, B, C)
(C, D, E)
Hint: Give an example of a relation r on schema R such that
a. Compute B+.
b. Prove (using Armstrong's axioms) that AF is a super key.
c. Compute a canonical cover for the above set of functional dependencies F; give each step of your derivation with an explanation.
d. Give a 3NF decomposition of r based on the canonical cover.
e. Give a BCNF decomposition of r using the original set of functional dependencies.
f. Can you get the same BCNF decomposition of r as above, using the canonical cover?