# BCFN Normal Form

• When a prime or a non prime attributes start determining the prime attributes of a table then that table is not in BCNF Normal Form

Example

• R(A, B, C)
• Functional Dependency
• AB–>C
• C–>B
• Determining candidate keys by checking closure
• (A)+ = A –> Not a candidate key
• (AB)+ = ABC –> Candidate key
• (AC)+ = ABC –> Candidate key
• Determining Prime and non prime attribute
• Prime : ABC
• Non Prime : None
• If the relation is in 2NF
• AB determines C but AB is not a part of candidate key but the entire candidate key
• C determines B but B is not a non prime attribute.
• So the relation R is in 2NF
• If the relation is in 3NF
• by definition when a non prime attributes starts determining other non prime attributes we call it Transitive dependency which is not allowed in 3NF
• In our case C determines B but both B and C are prime attributes
• So the relation R is in 3NF
• If the relation is in BCNF
• When a prime or a non prime attributes start determining the prime attributes of a table then that table is not in BCNF Normal Form
• And yes C is a prime attribute that is determining B which is also a prime attribute then relation R is not in BCNF

Reference :

Example 1