Relationships Among Normal Forms

Relationships Among Normal Forms

As we have pointed out, 4NF implies BCNF, which in turn implies 3NF. Therefore, the sets of relation schemas (including dependencies) satisfying the three normal forms are related as in the following figure (a). That is, if a relation with certain dependencies is in 4NF, it is also in BCNF and 3NF. Also, if a relation with certain dependencies is in BCNF, then it is in 3NF.

4NF implies BCNF implies 3NF

One more way to contrast the normal forms is by the guarantees they make about the set of relations that result from a decomposition into that normal form. These observations are summarized in the table of the following figure (b). That is, BCNF (and therefore 4NF) eliminates the redundancy and other anomalies that are caused by FD's, while only 4NF eliminates the additional redundancy that is caused by the presence of nontrivial MVD's that are not FD's. Sometimes, 3NF is sufficient to eliminate this redundancy, but there are examples where it is not. A decomposition into 3NF can always be chosen so that the FD's are preserved; that is, they are enforced in the decomposed relations (although we have not discussed the algorithm to do so in this blog). BCNF does not guarantee preservation of FD's, and none of the normal forms guarantee preservation of MVD's, though in usual cases the dependencies are preserved.

Properties of normal forms and their decompositions