CODEWITHSUNDEEP
database-normalizationfunctional-dependencies3nfcandidate-key
Marc
Marc

Reputation: 45

Definition for relation to be in 3NF using canonical cover

We are using following definition of 3NF:

A schema R is in third normal form (3NF) if for all FD α → β in F +, at least one of the following holds:

  1. α → β is trivial (i.e., β ⊆ α).
  2. α is a superkey for R
  3. Each attribute A in β – α is contained in a candidate key for R (prime).

I don't understand the third condition for this definition. OK, each atribute A in β –β – α means? What set of attributes does it include? α is contained in candidate key of R. What set of attributes does it include?

Upvotes: 0

Views: 202

Answers (1)

Renzo
Renzo

Reputation: 27424

β – α is the set of the attributes β minus the attributes that are in α, if any. So the third rule says that we can have attributes determinated by something which is not a superkey, but only if those attributes are primes (i.e. part of a candidate key), and obviously are not already in the determinant α (otherwise we have a trivial dependency).

So, when a relation schema is not in third normal form? When all the three conditions are false: that is when we have at least a non-trivial dependency whose determinant is not a superkey (so neither a candidate key) and whose right part contains attributes that are not prime.

Upvotes: -1

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