Understanding 3NF: plain English please

Question

I am working through an example problem in which we are trying to identify which of the following relations is in Third Normal Form (3NF). Here are the relations we are given:

Answer 1

A simplified expression of 3NF is "A relation is in 3NF if every attribute transitively dependent on a key is a key attribute."¹ A key attribute is an attribute that's part of any candidate key.

R₃ is one of the simpler ones to analyze with respect to 3NF.

R₃(ABCD)

• C -> B
• A -> B
• CD -> A
• BCD -> A

The only candidate key is CD.

• Is there a transitive dependency? Yes, there is: CD->A, and A->B. B is transitively dependent on the key.
• Is B a key attribute? No, it's not; CD is the only key.

So R₃ is not in 3NF.

R₄ is similar. C is the only candidate key.

• Is there a transitive dependency? Yes, there is: C->B, and B->A.
• Is A a key attribute? No, it's not; C is the only key.

So R₄ is not in 3NF.

In R₁, the candidate keys are AC and AD.

• Is there a transitive dependency? Yes, there is: AC->D, and D->C.
• Is C a key attribute? Yes, it is.

So R₁ is in 3NF.

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1. "A New Normal Form for the Design of Relational Schemata", Carlo Zaniolo, in ACM Transactions on Database Systems, Vol. 7, No. 3, September 1982, p 492. More recent work uses prime attribute to refer to attributes that are part of any candidate key and non-prime attribute to refer to attributes that are not part of any candidate key.