Suppose you are given a relation R with four attributes ABCD. For each of the following sets of FDs, assuming those are the only dependencies that hold for R, do the following:
(a) Identify the candidate key(s) for R.
(b) Identify the best normal form that R satisfies (1NF, 2NF, 3NF, or BCNF).
(c) If R is not in BCNF, decompose it into a set of BCNF relations that preserve the dependencies.
1. C → D, C → A, B → C
2. B → C, D → A
3. ABC → D, D → A
4. A → B, BC → D, A → C
5. AB → C, AB → D, C → A, D → B