Final answer:
The 3NF and BCNF are both forms of database normalization, with BCNF being a stricter subset of 3NF. While all BCNF tables are in 3NF, not all 3NF tables are in BCNF due to BCNF's requirement that every determinant must be a candidate key.
Step-by-step explanation:
The relationship between the 3rd Normal Form (3NF) and the Boyce-Codd Normal Form (BCNF), both used in the normalization process of database design, relates to the level of redundancy each form reduces. The 3NF is focused on eliminating transitive dependencies; that is, when a non-prime attribute depends on another non-prime attribute rather than depending solely on the primary key.
BCNF is a stricter version of 3NF. For a table to meet BCNF, it must first satisfy all the rules of 3NF. Additionally, in BCNF, for any non-trivial functional dependency X -> Y, X must be a superkey. This means that all determinants in BCNF are candidate keys. While all tables in BCNF are also in 3NF, the converse is not always true; a table in 3NF is not necessarily in BCNF, especially if it contains certain types of functional dependencies that are allowed in 3NF but not in BCNF.
Understanding these concepts is vital when designing a database to ensure data integrity and minimize redundancy. Tables in BCNF usually offer better protection against logical inconsistencies and anomalies than those in 3NF.