E212d9a797dbms chapter3 b.sc2 (2)

Module III: Relational Model
Objects

Contents
Domains and Relations, Relations and
predicates, Relational Data Integrity ; Primary
Key, Candidate Key , Foreign Key and their
rules; Relational operators, Relational
Algebra, Relational Calculus, SQL Language,
Data definition, Data retrieval and update
operations.

What are the Different types of
Keys in RDBMS ?
• Alternate key - An alternate key is any candidate key which is not selected to be
the primary key

• Candidate key - A candidate key is a field or combination of fields that can act
as a primary key field for that table to uniquely identify each record in that table.

• Compound key - compound key (also called a composite key or concatenated
key) is a key that consists of 2 or more attributes.

• Primary key - a primary key is a value that can be used to identify a unique row
in a table. Attributes are associated with it. Examples of primary keys are Social
Security numbers (associated to a specific person) or ISBNs (associated to a
specific book).

• In the relational model of data, a primary key is a candidate key chosen as the main
method of uniquely identifying a tuple in a relation.

• Superkey - A superkey is defined in the relational model as a set of attributes of a
relation variable (relvar) for which it holds that in all relations assigned to that
variable there are no two distinct tuples (rows) that have the same values for the
attributes in this set. Equivalently a superkey can also be defined as a set of
attributes of a relvar upon which all attributes of the relvar are functionally
dependent.

• Foreign key - a foreign key (FK) is a field or group of fields in a database record
that points to a key field or group of fields forming a key of another database record
in some (usually different) table. Usually a foreign key in one table refers to the
primary key (PK) of another table. This way references can be made to link
information together and it is an essential part of database normalization

Relational Algebra
• The basic set of operations for the relational model is known
as the relational algebra. These operations enable a user to
specify basic retrieval requests.

• The result of a retrieval is a new relation, which may have
been formed from one or more relations. The algebra
operations thus produce new relations, which can be further
manipulated using operations of the same algebra.

• A sequence of relational algebra operations forms a
relational algebra expression, whose result will also be a
relation that represents the result of a database query (or
retrieval request).

Unary Relational Operations
• SELECT Operation

SELECT operation is used to select a subset of the tuples from a relation that
satisfy a selection condition. It is a filter that keeps only those tuples that
satisfy a qualifying condition – those satisfying the condition are selected
while others are discarded.
Example: To select the EMPLOYEE tuples whose department number is
four or those whose salary is greater than $30,000 the following notation is
used:
σ DNO = 4 (EMPLOYEE)
σ SALARY > 30,000 (EMPLOYEE)
In general, the select operation is denoted by σ <selection condition>(R) where the
symbol σ (sigma) is used to denote the select operator, and the selection
condition is a Boolean expression specified on the attributes of relation R

(cont.)

(cont.)
• PROJECT Operation
This operation selects certain columns from the table and discards the other
columns. The PROJECT creates a vertical partitioning – one with the needed
columns (attributes) containing results of the operation and other containing
the discarded Columns.
Example: To list each employee’s first and last name and salary, the
following is used:
π (EMPLOYEE)
LNAME, FNAME,SALARY

π
The general form of the project operation is <attribute list>(R) where π
(pi) is the symbol used to represent the project operation and <attribute list>
is the desired list of attributes from the attributes of relation R.
The project operation removes any duplicate tuples, so the result of the
project operation is a set of tuples and hence a valid relation.

Unary Relational Operations (cont.)
• Rename Operation
We may want to apply several relational algebra operations one after the other.
Either we can write the operations as a single relational algebra expression
by nesting the operations, or we can apply one operation at a time and create
intermediate result relations. In the latter case, we must give names to the
relations that hold the intermediate results.
Example: To retrieve the first name, last name, and salary of all employees
who work in department number 5, we must apply a select and a project
operation. We can write a single relational algebra expression as follows:

π FNAME, LNAME, SALARY (σ DNO=5 (EMPLOYEE))
OR We can explicitly show the sequence of operations, giving a name to each
intermediate relation:
DEP5_EMPS ← σ DNO=5 (EMPLOYEE)
RESULT ← π FNAME, LNAME, SALARY (DEP5_EMPS)

Relational Algebra Operations From
Set Theory
• UNION Operation
The result of this operation, denoted by R ∪ S, is a relation that includes all
tuples that are either in R or in S or in both R and S. Duplicate tuples are
eliminated.
Example: To retrieve the social security numbers of all employees who either
work in department 5 or directly supervise an employee who works in
department 5, we can use the union operation as follows:
DEP5_EMPS ← σ DNO=5 (EMPLOYEE)
RESULT1 ← π SSN (DEP5_EMPS)
RESULT2(SSN) ← π SUPERSSN(DEP5_EMPS)
RESULT ← RESULT1 ∪ RESULT2
The union operation produces the tuples that are in either RESULT1 or
RESULT2 or both. The two operands must be “type compatible”.

Set Theory (cont.)
• INTERSECTION OPERATION

The result of this operation, denoted by R ∩ S, is a relation that includes all
tuples that are in both R and S. The two operands must be "type compatible"

Example: The result of the intersection operation (figure below) includes
only those who are both students and instructors.

STUDENT ∩ INSTRUCTOR

Set Theory (cont.)
• Set Difference (or MINUS) Operation
The result of this operation, denoted by R - S, is a relation that includes all
tuples that are in R but not in S. The two operands must be "type compatible”.

Example: The figure shows the names of students who are not instructors,
and the names of instructors who are not students.

STUDENT-INSTRUCTOR

INSTRUCTOR-STUDENT

Set Theory (cont.)
• CARTESIAN (or cross product) Operation
– This operation is used to combine tuples from two relations in a
combinatorial fashion. In general, the result of R(A1, A2, . . ., An) x
S(B1, B2, . . ., Bm) is a relation Q with degree n + m attributes Q(A1,
A2, . . ., An, B1, B2, . . ., Bm), in that order. The resulting relation Q
has one tuple for each combination of tuples—one from R and one
from S.
– Hence, if R has nR tuples (denoted as |R| = nR ), and S has nS
tuples, then
| R x S | will have nR * nS tuples.
– The two operands do NOT have to be "type compatible”

Example:
FEMALE_EMPS ← σ SEX=’F’(EMPLOYEE)
EMPNAMES ← π FNAME, LNAME, SSN (FEMALE_EMPS)

Binary Relational Operations
• JOIN Operation
– The sequence of cartesian product followed by select is
used quite commonly to identify and select related tuples
from two relations, a special operation, called JOIN. It is
denoted by a
– This operation is very important for any relational
database with more than a single relation, because it
allows us to process relationships among relations.
– The general form of a join operation on two relations
R(A1, A2, . . ., An) and S(B1, B2, . . ., Bm) is:
R S
<join condition>

where R and S can be any relations that result from general
relational algebra expressions.

Binary Relational Operations
(cont.)
Example: Suppose that we want to retrieve the name of
the manager of each department. To get the manager’s
name, we need to combine each DEPARTMENT tuple
with the EMPLOYEE tuple whose SSN value matches
the MGRSSN value in the department tuple. We do this
by using the join operation.
DEPT_MGR ← DEPARTMENT MGRSSN=SSN
EMPLOYEE

Binary Relational Operations (cont.)
• EQUIJOIN Operation
The most common use of join involves join conditions with equality comparisons only.
Such a join, where the only comparison operator used is =, is called an EQUIJOIN. In
the result of an EQUIJOIN we always have one or more pairs of attributes (whose
names need not be identical) that have identical values in every tuple.
The JOIN seen in the previous example was EQUIJOIN.

• NATURAL JOIN Operation
Because one of each pair of attributes with identical values is superfluous, a new
operation called natural join—denoted by *—was created to get rid of the second
(superfluous) attribute in an EQUIJOIN condition.
The standard definition of natural join requires that the two join attributes, or each pair
of corresponding join attributes, have the same name in both relations. If this is not the
case, a renaming operation is applied first.

Binary Relational Operations (cont.)
• DIVISION Operation
– The division operation is applied to two relations
R(Z) ÷ S(X), where X subset Z. Let Y = Z - X (and
hence Z = X ∪ Y); that is, let Y be the set of attributes
of R that are not attributes of S.
– The result of DIVISION is a relation T(Y) that includes
a tuple t if tuples tR appear in R with tR [Y] = t, and with
tR [X] = ts for every tuple ts in S.

– For a tuple t to appear in the result T of the DIVISION,
the values in t must appear in R in combination with
every tuple in S.

Examples of Queries in Relational
• Q1: Retrieve the name Algebraof all employees who
and address
work for the ‘Research’ department.
RESEARCH_DEPT ← σ DNAME=’Research’ (DEPARTMENT)
RESEARCH_EMPS ← (RESEARCH_DEPT DNUMBER= DNOEMPLOYEE EMPLOYEE)
RESULT ← π FNAME, LNAME, ADDRESS (RESEARCH_EMPS)

• Q6: Retrieve the names of employees who have no
dependents.
ALL_EMPS ← π SSN(EMPLOYEE)
EMPS_WITH_DEPS(SSN) ← π ESSN(DEPENDENT)
EMPS_WITHOUT_DEPS ← (ALL_EMPS - EMPS_WITH_DEPS)
RESULT ← π LNAME, FNAME (EMPS_WITHOUT_DEPS * EMPLOYEE)

Relational Calculus
• A relational calculus expression creates a new relation, which is
specified in terms of variables that range over rows of the stored
database relations (in tuple calculus) or over columns of the
stored relations (in domain calculus).
• In a calculus expression, there is no order of operations to
specify how to retrieve the query result—a calculus expression
specifies only what information the result should contain. This is
the main distinguishing feature between relational algebra and
relational calculus.
• Relational calculus is considered to be a nonprocedural
language. This differs from relational algebra, where we must
write a sequence of operations to specify a retrieval request;
hence relational algebra can be considered as a procedural way
of stating a query.

Tuple Relational Calculus
• The tuple relational calculus is based on specifying a number of tuple variables. Each
tuple variable usually ranges over a particular database relation, meaning that the
variable may take as its value any individual tuple from that relation.
• A simple tuple relational calculus query is of the form
{t | COND(t)}
where t is a tuple variable and COND (t) is a conditional expression involving t. The
result of such a query is the set of all tuples t that satisfy COND (t).

Example: To find the first and last names of all employees whose salary is above
$50,000, we can write the following tuple calculus expression:

{t.FNAME, t.LNAME | EMPLOYEE(t) AND t.SALARY>50000}
The condition EMPLOYEE(t) specifies that the range relation of tuple variable t is
EMPLOYEE. The first and last name (PROJECTION π FNAME, LNAME) of each
EMPLOYEE tuple t that satisfies the condition t.SALARY>50000 (SELECTION
σ SALARY >50000 ) will be retrieved.

The Domain Relational Calculus
• Another variation of relational calculus called the domain relational calculus, or
simply, domain calculus is equivalent to tuple calculus and to relational algebra.
• The language called QBE (Query-By-Example) that is related to domain calculus was
developed almost concurrently to SQL at IBM Research, Yorktown Heights, New
York. Domain calculus was thought of as a way to explain what QBE does.
• Domain calculus differs from tuple calculus in the type of variables used in formulas:
rather than having variables range over tuples, the variables range over single values
from domains of attributes. To form a relation of degree n for a query result, we must
have n of these domain variables—one for each attribute.
• An expression of the domain calculus is of the form
{x1, x2, . . ., xn | COND(x1, x2, . . ., xn, xn+1, xn+2, . . ., xn+m)}
where x1, x2, . . ., xn, xn+1, xn+2, . . ., xn+m are domain variables that range over
domains (of attributes) and COND is a condition or formula of the domain relational
calculus.

Example Query Using Domain
•
Calculus
Retrieve the birthdate and address of the employee whose name is ‘John B.
Smith’.

Query :
{uv | (∃ q) (∃ r) (∃ s) (∃ t) (∃ w) (∃ x) (∃ y) (∃ z)
(EMPLOYEE(qrstuvwxyz) and q=’John’ and r=’B’ and s=’Smith’)}

• Ten variables for the employee relation are needed, one to range over the
domain of each attribute in order. Of the ten variables q, r, s, . . ., z, only u and
v are free.
• Specify the requested attributes, BDATE and ADDRESS, by the free domain
variables u for BDATE and v for ADDRESS.
• Specify the condition for selecting a tuple following the bar ( | )—namely, that
the sequence of values assigned to the variables qrstuvwxyz be a tuple of the
employee relation and that the values for q (FNAME), r (MINIT), and s
(LNAME) be ‘John’, ‘B’, and ‘Smith’, respectively.

SQL
• SQL Components (DDL, DML, DCL)
• SQL Constructs (Select…from…where…. group by….
having…. order by…)
• Nested tables
• Views
• correlated query
• Objects in Oracle.

Clauses in SQL
• WHERE
• STARTING WITH
• ORDER BY
• GROUP BY
• HAVING

Operators
• Operators are the elements you use
inside an expression to articulate how
you want specified conditions to
retrieve data
• Operators fall into six groups:
arithmetic, comparison, character,
logical, set, and miscellaneous.

Functions: Molding the Data You
Retrieve
• Functions in SQL enable you to perform
feats such as determining the sum of a
column or converting all the characters of
a string to uppercase.
• Aggregate functions
• Date and time functions
• Arithmetic functions
• Character functions
• Conversion functions
• Miscellaneous functions

Manipulating Data
• The INSERT statement
• The UPDATE statement
• The DELETE statement

Views
• Views, or virtual tables, can be used to
encapsulate complex queries. After a view
on a set of data has been created, you
can treat that view as another table.

E212d9a797dbms chapter3 b.sc2 (2)

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