Boyce-Codd Normal Form (BCNF)
This BCNF eliminates all redundant data that can be discovered based on functional dependencies.
Definition: Let there be a relation R.
Let F be the set of Functional Dependencies applicable on R.
Let F+ is a closure set of F.
Here, R is said to be in BCNF, if for every FD of the form α à β (α Í R and β Í R.) in F+ satisfies one of the following two conditions.
- α à β is a trivial functional dependency. (β Í α)
- α is a super key of R.
Example-1: Let R = (A, B, C, D, E) and AB be super keys and F = [ AD à D, AB à C ] Check whether the above (R, F) is in BCNF?
Output:
The first FD satisfies the first condition.
The second FD satisfies the second condition.
Hence, the above (R, F) is said to be in BCNF.
Example-2: Let R = (P, Q, R, S, T) and PQ be super keys and F = [ PQ à S, QS à T ] Check whether the above (R, F) is in BCNF?
Output: The first FD satisfies the second condition.
The second FD does not satisfy any condition.
Hence, the above (R, F) is NOT in BCNF.
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