Given a relation $R(A, B, C, D, E, F)$, with the following functional dependencies: $\{A \rightarrow BC, CD \rightarrow E, B \rightarrow D, E \rightarrow A\}$.
The objective is to decompose $R$ into 3NF relations.
So far, I have determined that the following candidate keys are present in the given relation: $AF$, $EF$, $CDF$ and $BCF$.
Since every attribute is present as a part of some candidate key, for every $X \rightarrow A$, $A$ will be part of some candidate key, and so R itself should be in 3NF.
Since the question explicitly, however, states that it is not in 3NF, I have got a little confused. Where am I going wrong? Is there something that I have not understood?