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RELATIONAL ALGEBRA AND CALCULUS

Relational Algebra Relational Calculus SQL

Embedded SQL QBE

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Relational algebra is a collection ofoperations to manipulate or access

relations.

It is a procedural (or abstract) language

with operations performed on one or moreexisting relations to derive result(another)relations without changing the originalrelation(s).

Relational algebra consists of set ofrelational operators.

Each operator has one or more relations as

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Eight operations were proposed by Dr.

Codd and these eight operators aredivided into the following two categories.

!) "et#theoretic operations

$) %ative relational operations.

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"et#theoretic operations ma&e use of thefact that tables are essentially sets of rows.

'here are four set#theoretical operations

!) %I%

$) I%'ER"EC'I%

*) DI++ERE%CE

,) -RDC'

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%ative Relational peration focuses on the

structure of the rows.

'here are four native relational operations

!) -REC'I%

$) "E/EC'I%

*) I%

,) DI0I"I%

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!"ID LOCATION NO"O#"BINS $!ONE

12#34! 3356I $44 4$$#$*!,789

12#34$ :/:6'6 *44 4**#$789;!<

12#34* 3356I ,44 4$$#$*!789$

12#34, :/:6'6 $44 4**#$9;$<!4

12#347 DE/2I !44 4!!#$;<,879

RELATION% ARE!OUSE

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SELECTION O$ERATOR is used to extract(select) entire rows (tuples) from somerelation ( a table).

e.g.

"E/EC' 12#ID %#+#5I%" -2%Efrom 16RE2"Ewhere /C6'I%=>3356I? into R!

orR! = "E/EC' 12#ID %#+#5I%" -2%E

from 16RE2"E where /C6'I% =>3356I?

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!"ID NO"O#"BINS $!ONE

12#34! $44 4$$#$*!,789

12#34* ,44 4$$#$*!789$

RELATION% R&

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e.g."E/EC' @

from 16RE2"Ewhere /C6'I%=>3356I? into R$

or

R$ = "E/EC' from 16RE2"Ewhere /C6'I% = >3356I?

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12#34! 3356I $44 4$$#$*!,789

12#34* 3356I ,44 4$$#$*!789$

RELATION% R'

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e.g."E/EC' @

from 16RE2"Ewhere /C6'I%=>3356I? and %#+#

5I%"=$44 into R*

orR* = "E/EC' from 16RE2"E

where /C6'I%=>3356I? and %#+#5I%"=$44

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12#34! 3356I $44 4$$#$*!,789

RELATION% ARE!OUSE

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$RO(ECTION O$ERATION is used to extractentire column (attributes) from some relation

( a table).

It constructs a new relation from some existingrelation by selecting only speciAed attributes of

the existing relation and eliminating duplicatetuples in the newly formed relation.

e.g.

-REC' 16RE2"E% 12#ID/C6'I%-2%EI%' R,

or

R, = -REC' 16RE2"E 0ER 12#ID

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!"ID LOCATION $!ONE

12#34! 3356I 4$$#$*!,789

12#34$ :/:6'6 4**#$789;!<

12#34* 3356I 4$$#$*!789$

12#34, :/:6'6 4**#$9;$<!4

12#347 DE/2I 4!!#$;<,879

RELATION% R)

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e.g.-REC' 16RE2"E

% /C6'I%I%' R7or

R7 = -REC' 16RE2"E 0ER

/C6'I%

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LOCATION

3356I

:/:6'6

DE/2I

RELATION% R*

'he relation R7 eliminate one

duplicate tuple.

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(OINING O+eration is a method ofcombining two or more relations in asingle relation.

It brings together rows (tuples) from

diBerent relations (or tables) based on thetruth of some speciAed condition.

It is the most useful of all the relational

algebra operations.

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12#34! 3356I $44 4$$#$*!,789

12#34$ :/:6'6 *44 4**#$789;!<

12#34* 3356I ,44 4$$#$*!789$

12#34, :/:6'6 $44 4**#$9;$<!4

12#347 DE/2I !44 4!!#$;<,879

RELATION% ARE!OUSE

Considering the following two relations.

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!"ID ITE,"NO QT-

12#34! $7 87

12#34$ $8 74

12#34* $9 *4

12#34, $7 77

12#347 $; ,7

RELATION% ITE,S

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%ow we can oin the two relations

16RE2"E and I'E3" using thecommon attributes 12#ID.

I% 16RE2"E

1I'2 I'E3"% 12#IDInto R8

or

R8 = I% 16RE2"EI'E3" 0ER12#ID

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!"ID LOCATION

NO"O#"BINS

$!ONE ITE,"NO QT-

12#34!

3356I $44 4$$#$*!,789

$7 87

12#34$

:/:6'6 *44 4**#$789;!<

$8 74

12#34*

3356I ,44 4$$#$*!789$

$9 *4

12#

34,

:/:6'6 $44 4**#

$9;$<!4

$7 77

12#347

DE/2I !44 4!!#$;<,879

$; ,7

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UNION O$ERATION of two table (orrelations) is the every row (tuple) that

appears in either( or both) of the tables.

'he tables (or relations) on which it operatesmust contain the same number of columns(attributes).

If R and " have : and / tuples respectively

%I% is obtained by concatenating theminto one relation with maximum of (:/)tuples.

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!"ID LOCATION $!ONE

12#34! 3356I 4$$#$*!,789

12#34, :/:6'6 4**#$9;$<!4

12#347 DE/2I 4!!#$;<,879

RELATION% R.

!"ID LOCATION $!ONE

12#34! 3356I 4$$#$*!,789

12#34$ :/:6'6 4**#$789;!<

12#34, :/:6'6 4**#$9;$<!4

RELATION% R/

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%I% R;R<Into R!4

R

R!4 = %I% R;R<

!"ID LOCATION $!ONE

12#34! 3356I 4$$#$*!,789

12#34$ :/:6'6 4**#$789;!<

12#34, :/:6'6 4**#$9;$<!4

12#347 DE/2I 4!!#$;<,879

RELATION% R/

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DI##ERENCE O+erator subtracts fromthe Arst named relation (or table) those

tuples (rows) that appear in the secondnamed relation (or table) and create anew relation.

DI++ERE%CE R;R<Into R!4

or

R!4 = DI++ERE%CE R;R<

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!"ID LOCATION $!ONE

12#34! 3356I 4$$#$*!,789

12#34, :/:6'6 4**#$9;$<!4

12#347 DE/2I 4!!#$;<,879

RELATION% R.

!"ID LOCATION $!ONE

12#34! 3356I 4$$#$*!,789

12#34$ :/:6'6 4**#$789;!<

12#34, :/:6'6 4**#$9;$<!4

RELATION% R/

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!"ID LOCATION $!ONE

12#347 DE/2I 4!!#$;<,879

RELATION% R&0

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INTERSECTION O+erator selects only

those rows (tuples) that appear in both ofthe named relations (tables) .

I%'ER"EC'I% R;R<

Into R!!

or

R!! = I%'ER"EC'I% R; R<

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!"ID LOCATION $!ONE

12#34! 3356I 4$$#$*!,789

12#34, :/:6'6 4**#$9;$<!4

12#347 DE/2I 4!!#$;<,879

RELATION% R.

!"ID LOCATION $!ONE

12#34! 3356I 4$$#$*!,789

12#34$ :/:6'6 4**#$789;!<

12#34, :/:6'6 4**#$9;$<!4

RELATION% R/

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!"ID LOCATION $!ONE

12#34! 3356I 4$$#$*!,789

12#34, :/:6'6 4**#$9;$<!4

RELATION% R&&

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CARTESIAN $RODUCT perator (also

called Cross#-roduct) It ta&es each tuple(row) from the Arst named table (relation)and concatenates it with every row (tuple)of the second table (relation).

C6R'E"I6% -RDC' R!$ R!*Into R!,

or

R!, = C6R'E"I6% -RDC' R!$R!*

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!"ID LOCATION

12#34! 3356I

12#34, :/:6'6

RELATION% R&'

$ART"NA,E QT-

DR3-ER !4

DRI// ,4

1E/DI% $7

RELATION% R&1

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!"ID LOCATION $ART"NA,E QT-

12#34! 3356I DR3-ER !4

12#34! 3356I DRI// ,4

12#34! 3356I 1E/DI% $7

12#34, :/:6'6 DR3-ER !4

12#34, :/:6'6 DRI// ,4

12#34, :/:6'6 1E/DI% $7

RELATION% R&)

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DI2ISION O+eration is useful for a

particular type of Fuery that occurs FuitefreFuently in database applications.

Considering the two relations R!7 R!8

DI0I"I% R!7 R!8I%' R!9

RR!9 = DI0I"I% R!7 R!8

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E,$LO-EE LOCATION

:/G "G"'E3" 63"2ED-R

'RI%I'G /'D. :/:6'6

:/G "G"'E3" 3356I

C%CE-' "26-ER 63"2ED-R

'RI%I'G /'D. DE/2I

C%CE-' "26-ER DE/2I

C%CE-' "26-ER :/:6'6

RELATION% R&*

LOCATION

63"2ED-R

DE/2I

RELATION%R&3

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E,$LO-ERC%CE-' "26-ER

RELATION%R&4

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