Why is this relation not in Boyce-Codd Normal Form (BCNF)?

Question

I have the relation (A,B,C,D,E).

The relevant functional dependencies are:

• { E,B,C } → { D }
• { A,B } → { C }
• { E,B,D } → { C }
• { E,A,B } → { D }

The candidate key is (E,A,B).

I do not understand why this relation is not in BCNF, because the candidate key and its attributes are only elements on the left. Thanks a lot for any help!

Answer 1

C is a non-prime attribute (not part of the candidate key), and C depends on (A,B), which is a proper subset of the candidate key.

So the table is not in second normal form by definition.

Since BCNF implies 3NF and 3NF implies 2NF, this implies that the table is not in BCNF.