Relational Algebra Operators in Database Management

NostraDavid · 2024-06-22 · Updated 2026-03-09 · 373 words

This article summarizes the symbols and operations of relational algebra as explained in a video from the CMU Database Group, a YouTube channel by Carnegie Mellon University.

Basic Relational Algebra Operators

σ (Selection)

Symbol: σ (Sigma)
Description: The Selection operator is used to filter rows based on a specified condition.
Example: σ_condition(relation)

π (Projection)

Symbol: π (Pi)
Description: The Projection operator selects specific columns from a table.
Example: π(column1, column2, ...)(relation)

∪ (Union)

Symbol: ∪ (Union)
Description: The Union operator combines the results of two tables, removing duplicates.
Example: relation1 ∪ relation2

∩ (Intersection)

Symbol: ∩ (Intersection)
Description: The Intersection operator returns only the rows that are present in both tables.
Example: relation1 ∩ relation2

− (Difference)

Symbol: − (Minus or Difference)
Description: The Difference operator returns the rows present in the first table but not in the second.
Example: relation1 − relation2

× (Cartesian Product)

Symbol: × (Cross or Cartesian Product)
Description: The Cartesian Product operator returns the Cartesian product of two tables.
Example: relation1 × relation2

⨝ (Join)

Symbol: ⨝ (Join)
Description: The Join operator combines rows from two tables based on a related column.
Example: relation1 ⨝ relation2

Additional Relational Algebra Operators

ρ (Rename)

Symbol: ρ (Rho)
Description: The Rename operator is used to rename the relation or attributes.
Example: ρ_{new_name}(relation)

← (Assignment)

Symbol: R ← S (Assignment)
Description: The Assignment operator assigns the result of a query to a relation variable.
Example: R ← σ_condition(relation)

δ (Duplicate Elimination)

Symbol: δ (Delta)
Description: The Duplicate Elimination operator removes duplicate rows from a relation.
Example: δ(relation)

γ (Aggregation)

Symbol: γ (Gamma)
Description: The Aggregation operator is used for aggregate functions such as SUM, COUNT, AVG, etc.
Example: γ(attribute, SUM(attribute))(relation)

τ (Sorting)

Symbol: τ (Tau)
Description: The Sorting operator sorts the relation by specified attributes.
Example: τ(attribute)(relation)

÷ (Division)

Symbol: ÷ (Division)
Description: The Division operator finds tuples in one relation that are related to all tuples in another relation.
Example: relation1 ÷ relation2

Sources

"F2023 #01 - Relational Model & Algebra (CMU Intro to Database Systems)" by CMU Database Group:

• Basic Relational Algebra Operators
• Additional Relational Algebra Operators

Addendum

I'm currently reading "E. F. Codd and Relational Theory (revised edition)" by C. J. Date, which introduces additional operators without specific symbols.