2. Suppose you are given a relation R with four attributes ABCD. For each of the following sets of FDs and super keys, do the following:

a. Identify the best normal form that R satisfies (1NF, 2NF, 3NF, or BCNF).

b. If R is not in BCNF, can you decompose it into a set of BCNF relations that preserve the FDs? Identify any FDs that could not be preserved from the decomposition.

i. Super keys: B

FDs: C -> D, C -> A, B -> C

ii. Super keys: BD

FDs: B -> C, D -> A

iii. Super keys: ABC, BCD

FDs: ABC -> D, D -> A

iv. Super keys: A

FDs: A -> B, BC -> D, A -> C

v. Super keys: AB, BC, CD, AD

FDs: AB -> C, AB -> D, C -> A, D -> B