Relational Algebra

Relational algebra is a procedural query language. Each operation takes relations as input and produces a relation.

Operation	Symbol	Meaning	SQL equivalent
Selection	σ	Filter rows	WHERE
Projection	π	Choose columns (removes duplicates)	SELECT DISTINCT cols
Union	∪	Rows in either	UNION
Set difference	−	Rows in R but not S	EXCEPT
Cartesian product	×	All combinations	CROSS JOIN
Rename	ρ	Rename relation/attributes	AS
Intersection	∩	Rows in both	INTERSECT
Natural join	⋈	Join on common attributes	NATURAL JOIN
Division	÷	"for all" queries	NOT EXISTS … NOT EXISTS

The first six (σ, π, ∪, −, ×, ρ) are the fundamental operations; the rest can be derived from them.

Examples

Employee(eid, name, salary, dno), Dept(dno, dname)

Text

1. Names of employees earning more than 50000:
   π name ( σ salary > 50000 (Employee) )

2. Names of employees working in 'CSE':
   π name ( σ dname = 'CSE' (Employee ⋈ Dept) )

3. Students who have taken ALL courses:
   π roll, cid (Enrolls) ÷ π cid (Course)

Union Compatibility

For ∪, ∩ and −, both relations must have the same number of attributes with compatible domains.

Track your progress through the DBMS course

← Prev Next →