Third Normal Form

Definition

Let R(A ₁,...,A _n ) be a relation schema and Σ a set of functional dependencies over R(A ₁,...,A _n ). An attribute A _i (i ∈{1,...,n}) is a prime attribute if A _i is an element of some key of R(A ₁,...,A _n ). Then specification (R, Σ) is said to be in Third Normal Form (3NF) if for every nontrivial functional dependency X → A implied by Σ, it holds that X is a superkey for R or A is a prime attribute [2].

Key Points

In order to avoid update anomalies in database schemas containing functional dependencies, 3NF was introduced by Codd in [2]. This normal form is defined in terms of the notions of prime attribute and key as shown above. For example, given a relation schema R(A, B, C) and a set of functional dependencies Σ = {AB → C,C → B}, it holds that (R(A, B, C), Σ) is in 3NF since AB is a superkey and C is a prime attribute (given that AC is a key for R). On the other hand, (S(A, B, C), Γ) is not in 3NF if Γ = {A → B}, since A is not a superkey for S and Bis not a prime...