Encyclopedia of Database Systems

Living Edition
| Editors: Ling Liu, M. Tamer Özsu

Second Normal Form (2NF)

  • Marcelo Arenas
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4899-7993-3_1263-2




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 second normal form (2NF) if for every nontrivial functional dependency X → A implied by Σ, it holds that A is a prime attribute or X is not a proper subset of any (candidate) key for R [1].

Key Points

In order to avoid update anomalies in database schemas containing functional dependencies, 2NF was introduced by Codd in [1]. 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 = {A → B}, it does not hold that (R(A, B, C), Σ) is in 2NF since B is not a prime attribute and A is a proper subset of the key AC. On the other hand, (S(A, B, C), Γ) is in 2NF if Γ = {A → B, B → C}, since A is a key (and thus it is not a proper subset of any candidate key) and B is not contained in any (candidate) key for S.

It should be noticed that relation schema S(A, B, C) above is in 2NF if Γ = {A → B, B → C}, although this schema is not in 3NF. In fact, 3NF is strictly stronger than 2NF; every schema in 3NF is in 2NF, but there exist schemas (as the one shown above) that are in 2NF but not in 3NF.


Recommended Reading

  1. 1.
    Further CEF. Normalization of the data base relational model. In: Data base systems. Englewood Cliffs: Prentice-Hall; 1972. p. 33–64.Google Scholar

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© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Pontifical Catholic University of ChileSantiagoChile