## Exercise 12: Identifying Normal Forms

Armstrong’s Axioms and rules for splitting and combining.

• Reflexivity: X ⊆ Y ⇒ Y → X
• Augmentation: X → Y ⇒ XZ → YZ ∀ Z
• Transitivity: X → Y ∧ Y → Z ⇒ X → Z
• Combining: X → Y ∧ X → Z ⇒ X → YZ
• Splitting: X → YZ ⇒ X → Y ⇒ X→ Z

Consider the relation R(A,B,C,D). For each of the following sets of FDs,

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

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 (3NF or BCNF) that R satisfies.

c) If R is not in BCNF, decompose it into a set of BCNF relations.