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.

  • $\begingroup$ Basically you should break it in only two relations. Once you break the table to resolve CD --> E, the other transitive dependency is automatically resolved because E is no longer part of the table which has B in it. $\endgroup$ – Navjot Singh Nov 2 '18 at 0:54

So My decomposition is lossless and preserving all dependencies but there is no need for relation R3(E, C, B) because we already have A which can derive B in R1.

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