Relationship Between 3NF and BCNF
Zaniolo demonstrates that BCNF is strictly stronger than 3NF with an elegant proof. First, consider his definition of 3NF.
Let R be a relation variable, let X be any subset of the attributes of R, and let A be any single attribute of R.
R is in 3NF iff for every functional dependency X→ A in R, at least one of the following assertions is true:
If the third assertion is eliminated from consideration, the definition for BCNF follows, clearly indicating that BCNF is a stronger form than 3NF. Note that the third assertion constitutes the inadequacy of the original formulation of 3NF proposed by Codd.