Consider the following collection of relations and dependencies. Assume that each relation is obtained through decomposition from a relation with attributes ABCDEFGHI and that all the known dependencies over relation ABCDEFGHI are listed for each question. (The questions are independent of each other, obviously, since the given dependencies over ABCDEFGHI are different.) For each (sub) relation:
(a) State the strongest normal form that the relation is in.
(b) If it is not in BCNF, decompose it into a collection of BCNF relations.
1. R1(A,C,B,D,E), A → B, C → D
2. R2(A,B,F), AC → E, B → F
3. R3(A,D), D → G, G → H
4. R4(D,C,H,G), A → I, I → A
5. R5(A,I,C,E)