1. The Information Rule

All information in a relational database is represented explicitly at the logical level and in exactly one way – by values in tables. This rule emphasizes the importance of tables as the primary means of data representation, ensuring data is accessible and manageable in a structured format.

2. Guaranteed Access Rule

This rule states that every datum (atomic value) is guaranteed to be logically accessible by resorting to a combination of table name, primary key value, and column name. It underscores the necessity of unique keys for the retrieval of specific pieces of data, eliminating ambiguity in data access.

3. Systematic Treatment of Null Values

The DBMS must allow each field to remain null, which is a method to represent missing or inapplicable information consistently. This rule is crucial for handling cases where some data elements are unknown or irrelevant.

4. Dynamic On-line Catalog Based on the Relational Model

The database description is maintained in an online catalog, known as the system catalog or data dictionary, which is accessible to authorized users using the same query language used for regular data. This ensures that database metadata can be queried and managed with the same tools as the data itself.

5. The Comprehensive Data Sublanguage Rule

A relational system may support several languages and various modes of terminal use. However, it must support at least one declarative language (like SQL) that includes facilities for database definition (DDL), manipulation (DML), security, and integrity constraints. This rule advocates for the versatility and comprehensiveness of the database language.

6. The View Updating Rule

All views that are theoretically updatable must be updatable through the system. This rule deals with the ability of the system to update data through different views, ensuring data integrity and consistency across different perspectives of the database.

7. High-level Insert, Update, and Delete

The capability to handle a base relation or a derived relation as a single operand applies not only to retrieval but also to insert, update, and delete operations. This rule highlights the importance of treating data manipulation operations uniformly, regardless of whether they act on actual tables or the results of queries.

8. Physical Data Independence

Changes to the physical level (how the data is stored) should not require a change to an application based on the structure. This principle ensures that the data can be managed and optimized without affecting the application's logic.

9. Logical Data Independence

Changes to the logical level (tables, columns, rows) should not require a change to an application based on the structure. This rule emphasizes the ability to adapt the logical schema without altering the external schema or applications.

10. Integrity Independence

Integrity constraints specific to a particular relational database must be definable in the relational data sublanguage and storable in the catalog, not in the application programs. This rule ensures that the database maintains its integrity independently of applications that use it.

11. Distribution Independence

A relational DBMS has the capability to manage a database over a distributed network as if it were all stored on the same computer. This rule is aimed at supporting distributed database systems, which are increasingly common in enterprise environments.

12. The Non-subversion Rule

If a relational system has a low-level (single record at a time) language, that low level cannot be used to subvert or bypass the integrity rules and constraints expressed in the higher-level relational language (multiple records at a time). This rule safeguards the integrity constraints enforced at a higher level from being violated by lower-level operations.

1. The Information Rule in Action

In a retail database, product information is stored in tables, making it easily accessible and updatable. For instance, a 'Products' table would include columns for product ID, name, price, and stock levels. This organizational structure directly reflects the Information Rule, allowing for efficient data management and retrieval.

2. Ensuring Guaranteed Access

Consider a university database where each student's record is uniquely identified by a Student ID. To retrieve a student's information, one would use the Student ID as the key, along with the table name and the specific information needed (e.g., the student's major), ensuring precise data access as per the Guaranteed Access Rule.

3. Handling Null Values

In a medical database, not all patients will have a value for 'last surgery date'. In such cases, the field can remain null, demonstrating the Systematic Treatment of Null Values. This allows for accurate representation of patient records, even when some information is unavailable.

4. Dynamic On-line Catalog Utilization

Database administrators often query the system catalog to retrieve metadata, such as table structures or user permissions. This is a direct application of the Dynamic On-line Catalog Rule, enabling efficient database management and optimization.

5. Comprehensive Data Sublanguage Implementation

SQL, as a comprehensive data sublanguage, is used to perform various operations like creating tables, inserting data, and defining security rules. This illustrates the Comprehensive Data Sublanguage Rule by providing a unified approach to database manipulation and definition.

6. View Updating for Data Consistency

In a sales database, a view might be created to summarize sales by region. If the underlying data changes, the view should automatically update to reflect these changes, maintaining data consistency as outlined in the View Updating Rule.

7. Unified Data Manipulation

Whether inserting records into a base table or updating records resulting from a query, the approach remains consistent. This uniform treatment of data manipulation, irrespective of the operation's complexity, aligns with the High-level Insert, Update, and Delete Rule.

8. Adaptation to Physical and Logical Changes

When a database's storage mechanism is upgraded or when columns are added to a table, applications that use the database should not be affected. This adherence to Physical and Logical Data Independence ensures that the database can evolve without disrupting applications.

9. Integrity and Distribution Independence

Integrity constraints, such as ensuring that all email addresses in a 'Users' table are unique, are defined within the database itself and not in the application code. Similarly, the ability to manage data across multiple servers seamlessly reflects Distribution Independence, highlighting the robustness and scalability of relational systems.

10. Protecting Data Integrity

The Non-subversion Rule ensures that low-level access methods cannot bypass business rules and integrity constraints defined at the database level. For instance, even if a user could technically modify a record directly, such actions would be constrained by higher-level rules to prevent inconsistency.