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Relational algebra

Relational algebra is a formal system for manipulating relations. Set of operations that can be carried out on a relations are the selection, the projection, the Cartesian product (also called the cross product or cross join), the set union, and the set difference.

Basic operators in relational algebra

Select	σ	selects a subset of tuples from relation
Project	π	deletes unwanted columns from relation
Union	∪	tuples in relation 1 plus tuples in relation 2
Set-difference	−	tuples in relation 1, but not in relation 2
Cartesian Product	×	allows to combine two relations

Selection

Selects a subset of tuples from relation

Written as: σ_P(r)

• P is the predicate for selection
• Can use comparison operators: =, ≠, , ≥
• Can combine multiple predicates using: ∧ (and), ∨ (or), ¬ (not)
• r is the input relation
• Result relation contains all tuples in r for which P is true
• Result schema is identical to schema for r

Now, we will apply select operation on student table.

Retrieve all tuples for students in the K12 grade.

σ_{grade = “K12”} (student)

Retrieve all tuples for students in the K12 grade, with fee under 7000

σ_{grade=“K12” ∧ fees<7000}(student)

Projection

To select vertical subset of a relation

Written as: Π_a,b,…(r)

• Specified attributes must actually be in schema of r
• Result’s schema only contains the specified attributes

Π_{roll_no,grade}(student)

 

Set Union

Written as: R1 ∪ R2

Result contains all tuples from R1 and R2

Each tuple is unique, even if it’s in both R1 and R2

Set Difference

Written as: R1 - R2

R1 – R2 returns a relation containing all tuples in R1 but not in R2

 

Cartesian Product

It operates on two relations and is denoted by X.

Cartesian product of two relation R1 and R2 is represented by R=R1X R2.

The degree of R is equal to sum of degrees of R1 and R2.

The cardinality of R is product of cardinality of R1 and cardinality of R2

 

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