I have a schema R = {A,B,C,D,E} and the set F of FDs:
F = {A --> BCDE, CD --> E, EC --> B}.
Candidate key = A Non - Prime Attributes = BCDE Prime Attributes = A
According to me, there is no partial dependency because no non-prime attribute is dependent on part of CK.
E and B are transitively dependent on A so the schema Ris not in 3NF.
Decomposing R into 3NF, I have three relations and three set of FDs :
R1(A,B,C,D) F1={A --> B,A --> C,A --> D}
R2(C,D,E) F2={CD --> E}
R3(E,C,B) F3={EC --> B}
My question is, Is my decomposition of R into 3NF is lossless and preserving all dependencies or not? And if not how can I decompose it into 3NF losslessly while preserving all dependencies.