Third Normal Form (3NF)

Definition: Let there be a relation R.

Let F is the set of Functional Dependencies applicable on R.

Let F+  is a closure set of F. Here, R is said to be in 3NF, if for every FD of the form α à β (α  ⊆  R  and   β  ⊆  R.) in F+ satisfies one of the following three conditions:

1. α →β  is a trivial functional dependency. (β ⊆ α)
2. α is a super key of R.                                                     
3. Every attribute A in β – α is contained in a candidate key R.

Example-1 :     

Let R = (A, B, C, D, E) and AB be super keys and F = [ AD →D, AB →C, CD → B ] Check whether the above (R, F) is in BCNF?

Output :  

The first FD satisfies the first condition.

The second FD satisfies the second condition. 

The third FD satisfies the third condition. 

Hence, the above (R, F) is said to be in 3NF.

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Third Normal Form (3NF)