Relational Algebra, was first created by Edgar F Codd while at IBM.

**Relational
Algebra in DBMS**

**What is Relational Algebra?**

Relational Algebra, was first created by ** Edgar
F Codd** while at IBM. It was used for modeling the data stored in
relational databases and defining queries on it.

Relational Algebra is a procedural query
language used to query the database tables using SQL.

Relational algebra operations are performed
recursively on a relation (table) to yield an output. The output of these
operations is a new relation, which might be formed by one or more input relations.

Relational Algebra is divided into various
groups

Unary Relational Operations

SELECT ( symbol : σ)

PROJECT ( symbol : ∏)

Relational Algebra Operations from Set Theory

·
UNION (∪)

·
INTERSECTION (∩)

·
DIFFERENCE (−)

·
CARTESIAN PRODUCT (X)

**SELECT (symbol : σ)**

General form σ_{c} ( R ) with a
relation R and a condition C on the attributes of R.

The SELECT operation is used for selecting a
subset with tuples according to a given condition.

Select filters out all tuples that do not
satisfy C.

STUDENT

σ_{course} = “Big Data” (STUDENT )

**PROJECT **(symbol :**
**Π)

The projection eliminates all attributes of the
input relation but those mentioned in the projection list. The projection method
defines a relation that contains a vertical subset of Relation.

**Example 1 **

Π_{course} (STUDENT)

Result

**Course**

Big Data

R language

Python Programming

**Example 2 (using Table 11.1)**

Π_{course} (STUDENT)

Result

**UNION (Symbol :**∪**)**

It includes all tuples that are in tables A or
in B. It also eliminates duplicates. Set A Union Set B would be expressed as A ∪ B

**Example 3**

Consider the following tables

**Result**

**SET DIFFERENCE ( Symbol : - )**

The result of A – B, is a relation which
includes all tuples that are in A but not in B.

The attribute name of A has to match with the
attribute name in B.

Example 4 ( using Table 11.2)

**INTERSECTION (symbol : **∩**) A **∩** B**

Defines a relation consisting of a set of all
tuple that are in both in A and B. However, A and B must be union-compatible.

Example 5 (using Table 11.2)

**PRODUCT OR CARTESIAN PRODUCT (Symbol : X )**

Cross product is a way of combining two
relations. The resulting relation contains, both relations being combined.

A x B means A times B, where the relation A and
B have different attributes.

This type of operation is helpful to merge
columns from two relations.

Cartesian product : Table A x Table B

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