Relational Algebra

Relational Algebra

Introduction

Relational algebra is a procedural query language used to query and manipulate data in relational databases.

It provides a foundation for SQL, and defines operations on relations (or tables) to produce new relations.

The key features are:

It is very important because it:

Query processing steps include:

Operation	Symbol	Example
`SELECT`	$\sigma$	$\sigma$ Status = “Active”(Customer)
`PROJECTION`	$\pi$	$\Pi$ CustomerName, Status (Customer)
`RENAME`	$\rho$	$\rho$ ${new_name} / ${old_name}
`UNION`	$\cup$	$A \cup B$ gives all tuples in table $A$ and $B$ .
`INTERSECTION`	$\cap$	$A \cap B$ gives all tuples both in $A$ and $B$ .
`DIFFERENCE`	$-$	$A - B$ gives tuples in $A$ but not in $B$ .
`CARTESIAN PRODUCT`	$\times$	$A \times B$ gives combinations of columns in $A$ and $B$ .
`JOIN`	$\Join$	None

Operations of modifying databases:

These operations are expressed using the assignment operator $\gets$ .

r \gets r - E

Example:

\text{Customer} \gets \text{Customer} - (\sigma \; \text{Status = `Active'(Customer)})

r \gets r \cup E

Example:

\text{Customer} \gets \text{Customer} \cup \{1, `\text{Name}', `\text{Active}'\}

Updating can be expressed by a sequence of deletion and insertion operations.

Last updated on May 31, 2026