WikiGalaxy
Selection (σ)
Definition:
Selection is a unary operation that selects tuples that satisfy a given predicate from a relation. It's denoted by σ.
Example Use Case:
Extracting records of employees who earn more than $50,000.
σ(salary > 50000)(Employee)
Result:
A subset of the Employee relation containing only those tuples where the salary is greater than 50,000.
Projection (π)
Definition:
Projection is a unary operation that extracts certain columns from a relation. It's denoted by π.
Example Use Case:
Retrieving only the names and salaries of employees.
π(name, salary)(Employee)
Result:
A new relation consisting of only the name and salary attributes of the Employee table.
Union (∪)
Definition:
Union is a binary operation that combines the tuples of two relations and removes duplicates. It's denoted by ∪.
Example Use Case:
Combining two sets of employee records from different departments.
Employee ∪ Manager
Result:
A relation containing all unique employee and manager records.
Set Difference (-)
Definition:
Set Difference is a binary operation that finds tuples present in one relation but not in another. It's denoted by -.
Example Use Case:
Identifying employees who are not managers.
Employee - Manager
Result:
A relation containing employees who do not appear in the Manager relation.
Cartesian Product (×)
Definition:
The Cartesian Product is a binary operation that returns a relation with all possible combinations of tuples from two relations. It's denoted by ×.
Example Use Case:
Generating all possible pairs of employees and departments.
Employee × Department
Result:
A relation containing all combinations of employee and department tuples.
Rename (ρ)
Definition:
Rename is a unary operation used to rename the output relation or its attributes. It's denoted by ρ.
Example Use Case:
Renaming the Employee relation to Staff.
ρ(Staff, Employee)
Result:
A relation identical to Employee but named Staff.
Join (⨝)
Definition:
Join is a binary operation that combines related tuples from two relations based on a common attribute. It's denoted by ⨝.
Example Use Case:
Linking employees with their respective departments.
Employee ⨝ Department
Result:
A relation containing tuples of employees linked with their departments.
Intersection (∩)
Definition:
Intersection is a binary operation that returns tuples present in both relations. It's denoted by ∩.
Example Use Case:
Finding employees who are also managers.
Employee ∩ Manager
Result:
A relation containing tuples that are common to both Employee and Manager relations.
