Minimal covers, also known as canonical covers, are an essential concept in Relational Database Management Systems (RDBMS) that help simplify and optimize the set of functional dependencies (FDs) in a database schema. A minimal cover represents a minimal and irreducible set of FDs that is equivalent to the original set of FDs. Here's how you can obtain a minimal cover in RDBMS:

1. Start with the given set of FDs.

2. Remove any redundant FDs from the set. A redundant FD is one that can be derived from other FDs in the set.

3. Apply the Armstrong's axioms to derive the closure of the remaining FDs.

4. For each FD in the closure set, check if it is redundant. If it can be removed without affecting the closure, it is redundant.

5. Repeat steps 3 and 4 until no further redundant FDs can be identified.

6. The resulting set of FDs is the minimal cover.

Here's an example to illustrate the process:

Given the set of FDs:
- A → B
- A → C
- AB → D
- C → D

1. Start with the given set: {A → B, A → C, AB → D, C → D}

2. Remove redundant FDs: {A → B, A → C, AB → D}

3. Apply Armstrong's axioms to derive the closure: {A → B, A → C, A → D, AB → D, C → D}

4. Check for redundancy: - A → B is not redundant.
- A → C is not redundant.
- A → D is redundant since it can be derived from A → B and AB → D.
- AB → D is not redundant.
- C → D is not redundant.

5. Remove redundant FDs: {A → B, A → C, AB → D, C → D}

6. The resulting minimal cover is: {A → B, A → C, AB → D, C → D}

The minimal cover ensures that no redundant or unnecessary FDs are present in the set. It represents the essential set of FDs required to preserve the dependencies in the database schema. Having a minimal cover simplifies the design, reduces redundancy, and improves data integrity in the database.

Obtaining a minimal cover is an important step in the normalization process and helps optimize the database design by eliminating unnecessary dependencies.

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