Third normal form and boyce-codd normal form a comparison

Difference between 3NF and BCNF

Assume the following things;

A and B are set of attributes.

A is non-key attribute and B is the primary key.

FD – { A → B. }

The above Functional Dependency is about the dependency of primary key on a non-key attribute. This functional dependency is permitted in Third Normal Form (3NF). 3NF tries to identify and eliminate Non-key → Non-key dependency.

This Functional Dependency is not permitted in Boyce-Codd Normal Form (BCNF), because BCNF expects the determiner should be a candidate key. In our example, A is not a candidate key. This is why BCNF is termed as strict 3NF.

3NF is always achievable. BCNF is not. BCNF may result in Loss-less Join Decomposition and lead to loss of Dependency Preserving Decompositions.

Properties	3NF	BCNF
*Achievability*	Always achievable	Not always achievable
*Quality of the tables*	Less	More
*Non-key Determinants*	Can have non-key attributes as determinants	Cannot have.
*Proposed by*	Edgar F. Codd	Raymond F.Boyce and Edgar F.Codd jointly proposed
*Decomposition*	Loss-less join decomposition can be achieved	Sometimes Loss-less join decomposition cannot be achieved