Relational Algebra in Database Management System.

Relation Algebra:

It is  a procedure language used to query different relations in a Relational Database. It takes instances of relation as input and gives instances of relation as output, which means the input to every relational algebraic expression will be a relational and output of expression will also be a relation.

Relation algebra provides a mathematical background using different mathematical operators along with relation from a database .

#Relation: Table

#Relationship: Natural Association 

It consists of following basic operators used to query over the relation:

1. SELECTION  (σ)

2. PROJECTION  (∏)

3. UNION  (∪)

4. SET DIFFERENCE  (−)

5. CARTESIAN PRODUCT  (Χ)

6. RENAME  (ρ)

SELECTION  (σ):

 It is a unary operators used to select tuples from a relation. It is define as follow :

σ     (r)

    ρ 

Where σ is operator 

 r is relation 

ρ is predicate which specify different condition using relational  operators and joining predicate such as AND ,OR.

Example:

An expression in σ is same as a query in SQL with select *; 

σ(Table_name)

or

SELECT * FROM Table_name.

PROJECTION  (∏)

Projection is a unary operators used to project columns over a relations which means projection is used to select columns from the specify relations.

It is define as follows:

∏                     (r);

    C1, C2 ,.......

∏is a operator

r is relation

C1, C2 and so on are the columns of relation r.

Example:

 ∏                                               (employee_table);

    employee_id, employee_name

or

SELECT employee_id , employee_name 

FROM employee_table;

UNION  (∪):

It is a binary operator that is always takes two relations say r and s where that  r and s must specify the following properties:  

1. Arity (Degree) of r and s must be same i.e number of columns on r and s must be same.

2. Domain of first column in r must be same to domain of first column in s i.e corresponding columns in R and S should have the same domain .

 It is denoted as :

 r  ∪ s

Where r and s are relation.

Example:

Write an expression to find out employee number if they have either sales more then quota or order amount more than 2500/-.

 ∏              (σ  sales > quota(salesrep))     <----- r

      emp_id

∪

 ∏    ( σ amount > 2500   (orders))   <------ s

     rep 

SET DIFFERENCE  (−):

It is a binary operator which takes two relations r and s and it is denoted as r - s ,where r and s must satisfy the following property:

1. Arity (degree ) of r and s must be same.

2. Domain of the first column of r must be same as first column of s.

3. When r - s is executed , then the output will have all tuples which are there in r but not in s.

Example:

Find out the employee id having sales more then quota and not accepted an order for more than 2500.

 ∏             (σ sales > quota (salsrep))

      emp_id 

_

∏             (σ amount > quota (orders)) ;

      rep

For Cartesian Product and Rename👇                                                                                                              https://languagecopy.blogspot.com/2020/07/cartesian-product-and-rename-concept-in.html