Database Integrity Constraints and Relational Algebra Operations
What are Integrity Constraints?
Integrity constraints are predefined rules used to maintain data quality. They ensure that data insertion, updates, and deletions are performed without affecting data integrity. These constraints act as guidelines, ensuring data accuracy and consistency, thus protecting databases.
Types of Integrity Constraints:
- Domain Constraints
- Not-Null Constraints
- Entity Integrity Constraints
- Key Constraints
- Primary Key Constraints
- Referential Integrity Constraints
Importance of Referential Integrity Constraints:
- Maintains Consistent Relationships: Referential integrity ensures that foreign key values correspond to valid primary key values, preventing orphaned records.
- Prevents Data Anomalies: It avoids duplicate records and mismatched data, ensuring accurate data retrieval and reporting.
- Supports Data Integrity: Changes to primary keys are correctly propagated to related tables, or blocked if integrity is compromised.
- Enhances Query Accuracy: Queries joining tables based on foreign keys are more reliable and produce correct results.
- Facilitates Data Management: It simplifies data management, handling cascading updates or deletions automatically.
- Enforces Business Rules: Referential integrity ensures data relationships reflect real-world associations, such as an order referencing an existing customer.
Relational Algebra Operations for Set Theory
UNION, INTERSECTION, and MINUS Operations:
The UNION, INTERSECTION, and MINUS Operations:
- UNION: (R ∪ S) includes all tuples in R or S or both, with duplicates eliminated.
- INTERSECTION: (R ∩ S) includes all tuples in both R and S.
- SET DIFFERENCE (or MINUS): (R – S) includes all tuples in R but not in S.
These are binary operations applied to two sets of tuples. For relational databases, the two relations must have the same type of tuples, known as union compatibility or type compatibility.
Two relations R(A1, A2, …, An) and S(B1, B2, …, Bn) are union compatible if they have the same degree n and if dom(Ai) = dom(Bi) for 1 ≤ i ≤ n. This means they have the same number of attributes, and each corresponding pair of attributes has the same domain.
CARTESIAN PRODUCT (CROSS PRODUCT) Operation:
The CARTESIAN PRODUCT operation, also known as CROSS PRODUCT or CROSS JOIN, is denoted by x.
This binary set operation does not require union compatibility. It combines every tuple from one relation with every tuple from the other.
The result of R(A1, A2, …, An) x S(B1, B2, …, Bm) is a relation Q with degree n + m, attributes Q(A1, A2, …, An, B1, B2, …, Bm) in that order.
The resulting relation Q has one tuple for each combination of tuples from R and S. If R has m tuples and S has n tuples, then R x S will have m*n tuples.