To decompose the schema into 3NF based on the given functional dependencies, we can follow these steps:
Step 1: Start with the original relation R(A,B,C,D,E) and identify all the individual attributes that participate in functional dependencies.
- AB → C
- BC → D
- CD → E
- DE → A
Step 2: Check for any partial dependencies and remove them.
In this case, there are no partial dependencies.
Step 3: Check for transitive dependencies and remove them.
The dependency CD → E has a transitive dependency through AB. To remove it, we create a new relation with attributes from both sides of the dependency:
R1(C, D, E)
And remove CD from the original relation:
R’(A,B,CD,DE)
Step 4: Repeat steps 2 and 3 until no further decomposition is possible.
There are no more partial or transitive dependencies to consider in this case. Therefore, our final decomposition is:
R1(C, D, E) R2(A,B,CD,DE)
This decomposition satisfies the requirements of Third Normal Form (3NF), where each relation contains only attributes that are functionally dependent on the primary key.
内容由零声教学AI助手提供，问题来源于学员提问
