Relational Algebra in DBMS power ppoint pesenetation

Relational Algebra
• Relational algebra in DBMS is a procedural query language.
• Queries in relational algebra are performed
using operators. An operator can be either unary or binary.
• Relational Algebra is a procedural query language.
Relational algebra mainly provides a theoretical foundation
for relational databases and SQL.
• The main purpose of using Relational Algebra is to define
operators that transform one or more input relations into
an output relation.
• Relational Algebra came in 1970 and was given by Edgar F.
Codd (Father of DBMS). It is also known as Procedural
Query Language(PQL) as in PQL, a programmer/user has to
mention two things, "What to Do" and "How to Do".

Relational Operations in DBMS
• Relational algebra is a procedural query language.
It gives a step by step process to obtain the result
of the query.
• In Relational Algebra, we have two types of
Operations.
• Basic Operations
• Derived Operations
• Applying these operations over relations/tables
will give us new relations as output.

Select Operation (σ)
• Select (σ)
• Select operation is done by Selection Operator which is represented
by "sigma"(σ). It is used to retrieve tuples(rows) from the table where the
given condition is satisfied. It is a unary operator means it requires only
one operand.
• Notation : σ p(R)
• Where σ is used to represent SELECTION
• R is used to represent RELATION
• p is the logic formula
• Example: σ AGE=20 (STUDENT)
Types of Relational operation

Select Operation (σ)
• where σ stands for selecting tuples (rows) and r stands for
relation (table) name. p is prepositional logic formula which
may use connectors like and, or, and not. These terms may use
relational operators like = , ≠ , ≥ , < , > , ≤ .
• Example 1: σsubject = "database"(Books)
• Output : Selects rows whose subject is 'database' from books
table.
• Example 2: σ subject = "database" and price = "450"(Books)
• Output : Selects rows from books where subject is 'database'
and 'price' is 450.
• Example 3: σ subject = "database" and price = "450" or year
> "2010"(Books)
• Output : Selects rows from books where subject is 'database'
and 'price' is 450 or those books published after 2010.

Project Operation (∏)
• Project (∏)
• Project operation is done by Projection Operator which is
represented by "pi"(∏).
• It is used to retrieve certain attributes(columns) from the
table.
• It is also known as vertical partitioning as it separates the
table vertically. It is also a unary operator.
• Notation: ∏ A1, A2, … An (R)
• where A1, A2 , An are column (attribute) names of relation R.
• Duplicate rows are automatically eliminated in the output.
• Example: ∏ subject, author (Books)
• Display values from columns subject and author from the
relation Books.

Union Operation ( )
∪
• Union ( )
∪
• Union operation is done by Union Operator which is
represented by "union"( ).
∪
• It is the same as the union operator from set theory, i.e., it
selects all tuples from both relations but with the exception
that for the union of two relations/tables both relations must
have the same set of Attributes.
• It is a binary operator as it requires two operands.
Notation: R S
∪
Where R is the first relation
S is the second relation
• If relations don't have the same set of attributes, then the union of such
relations will result in NULL.
• ∏ NAME(STUDENT) ∏
∪ NAME(EMPLOYEE)

Intersection Operation (∩)
• Intersection (∩)
• Intersection operation is done by Intersection Operator which is
represented by "intersection"(∩).
• It is the same as the intersection operator from set theory, i.e., it selects
all the tuples which are present in both relations.
• It is a binary operator as it requires two operands. Also, it eliminates
duplicates.
Notation : R ∩ S
• Example : we want the names which are present in STUDENT as well as
in EMPLOYEE relation, Relations we used in Basic Operations.
• ∏ NAME(STUDENT) ∩ ∏ NAME(EMPLOYEE)

Set Difference (−)
• Set Difference (-)
• Set Difference as its name indicates is the difference
between two relations (R-S).
• It is denoted by a "Hyphen"(-) and it returns all the
tuples(rows) which are in relation R but not in relation S.
• It is also a binary operator.
Notation : R - S
• Just like union, the set difference also comes with the
exception of the same set of attributes in both relations.

Cartesian Product (Χ):
• Cartesian product (X)
• Cartesian product is denoted by the "X" symbol.
• we have two relations R and S. Cartesian product will combine
every tuple(row) from R with all the tuples from S.
• It is also a binary operator.
•
Notation: R X S
• Example: Π author (Books) X Π author (Articles)

Rename Operation (ρ)
• Rename (ρ)
• Rename operation is denoted by "Rho"(ρ).
• As its name suggests it is used to rename the output relation.
Rename operator too is a binary operator.
• Notation: ρ(R,S)
Where R is the new relation name
S is the old relation name
• we are fetching the names of students from STUDENT relation.
We would like to rename this relation as STUDENT_NAME.
• ρ(STUDENT_NAME,∏ NAME(STUDENT))

Overview
• Select (σ) is used to retrieve tuples(rows) based on certain
conditions.
• Project (∏) is used to retrieve attributes(columns) from the
relation.
• Union ( )
∪ is used to retrieve all the tuples from two
relations.
• Set Difference (-) is used to retrieve the tuples which are
present in R but not in S(R-S).
• Cartesian product (X) is used to combine each tuple from the
first relation with each tuple from the second relation.
• Rename (ρ) is used to rename the output relation.

Division (/):
• Division (÷)
• Division Operation is represented by "division"(÷
or /) operator and is used in queries that involve
keywords "every", "all", etc.
Notation : R(X,Y)/S(Y)
Here,
R is the first relation from which data is retrieved.
S is the second relation that will help to retrieve the
data.

• X and Y are the attributes/columns present in relation. We can have
multiple attributes in relation, but keep in mind that attributes of S must
be a proper subset of attributes of R.
• For each corresponding value of Y, the above notation will return us the
value of X from tuple<X,Y> which exists everywhere.
• It's a bit difficult to understand this in a theoretical way, but you will
understand this with an example.
• Let's have two relations, ENROLLED and COURSE. ENROLLED consist of
two attributes STUDENT_ID and COURSE_ID. It denotes the map of
students who are enrolled in given courses.
• COURSE contains the list of courses available.
• ENROLLED(STUDENT_ID, COURSE_ID)/COURSE(COURSE_ID)

SQL JOINS
• SQL Join statement is used to combine data or
rows from two or more tables based on a common
field between them. Different types of Joins are as
follows:
• INNER JOIN
• LEFT JOIN
• RIGHT JOIN
• FULL JOIN
• NATURAL JOIN

SQL JOINS
• JOIN is an SQL clause used to query and
access data from multiple tables, based on
logical relationships between those tables.

INNER JOIN
• A. INNER JOIN
• The INNER JOIN keyword selects all rows from both the tables as long as the
condition is satisfied. This keyword will create the result-set by combining all
rows from both the tables where the condition satisfies i.e value of the common
field will be the same.
• SELECT table1.column1,table1.column2,table2.column1,....
FROM table1
INNER JOIN table2
ON table1.matching_column = table2.matching_column;
table1: First table.
table2: Second table
matching_column: Column common to both the tables.

INNER JOIN
• Example Queries(INNER JOIN)
• This query will show the names and age of students enrolled in different
courses.
• SELECT StudentCourse.COURSE_ID, Student.NAME, Student.AGE FROM
Student
INNER JOIN StudentCourse
ON Student.ROLL_NO = StudentCourse.ROLL_NO;

LEFT JOIN
• B. LEFT JOIN
• This join returns all the rows of the table on the left side of the join
and matches rows for the table on the right side of the join. For the
rows for which there is no matching row on the right side, the result-
set will contain null. LEFT JOIN is also known as LEFT OUTER JOIN.
• Syntax:
FROM table1
LEFT JOIN table2

• Example Queries(LEFT JOIN):
• SELECT Student.NAME,StudentCourse.COURSE_ID
FROM Student
LEFT JOIN StudentCourse
ON StudentCourse.ROLL_NO = Student.ROLL_NO;
Output:
LEFT JOIN

RIGHT JOIN
• RIGHT JOIN
• RIGHT JOIN is similar to LEFT JOIN. This join returns all the rows of the table on
the right side of the join and matching rows for the table on the left side of the
join. For the rows for which there is no matching row on the left side, the result-
set will contain null. RIGHT JOIN is also known as RIGHT OUTER JOIN.
• Syntax:
FROM table1
RIGHT JOIN table2

• Example Queries(RIGHT JOIN):
FROM Student
RIGHT JOIN StudentCourse
Output:

FULL JOIN
• FULL JOIN
• FULL JOIN creates the result-set by combining results of both
LEFT JOIN and RIGHT JOIN. The result-set will contain all the
rows from both tables. For the rows for which there is no
matching, the result-set will contain NULL values.

FULL JOIN
• Syntax:
• SELECT
table1.column1,table1.column2,table2.column1,....
FROM table1
FULL JOIN table2

FULL JOIN
• Example Queries(FULL JOIN):
FROM Student
FULL JOIN StudentCourse
Output:
NAME COURSE_I
D
HARSH 1
PRATIK 2
RIYANKA 2
DEEP 3
SAPTARHI 1
DHANRAJ NULL
ROHIT NULL
NIRAJ NULL
NULL 4
NULL 5
NULL 4

Natural join
• E. Natural join (?)
• Natural join can join tables based on the common
columns in the tables being joined. A natural join returns
all rows by matching values in common columns having
same name and data type of columns and that column
should be present in both tables.
• Both table must have at list one common column with
same column name and same data type.
• The two table are joined using Cross join.
• DBMS will look for a common column with same name
and data type Tuples having exactly same values in
common columns are kept in result.

Natural join
Employee
Emp_id Emp_name Dept_id
1 Ram 10
2 Jon 30
3 Bob 50
Department
Dept_id Dept_name
10 IT
30 HR
40 TIS
Query: Find all Employees and their respective
departments.
Solution: (Employee) ? (Department)
Emp_id Emp_name Dept_id Dept_id Dept_name
1 Ram 10 10 IT
2 Jon 30 30 HR
Employee data Department data
Example:

Relational Algebra in DBMS power ppoint pesenetation

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