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Attribute Closure

The document explains the concept of attribute closure in the context of database management systems (DBMS), highlighting its importance in identifying candidate keys, checking functional dependencies, and normalization. It provides an example with a relation R containing attributes A, B, C, D, and E, along with their functional dependencies, and demonstrates how to derive attribute closures using rules such as reflexivity, transitivity, and union. The closure sets for individual attributes and combinations are also presented, showing the attributes that can be determined from each attribute.

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Sagar Giri
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82 views4 pages

Attribute Closure

The document explains the concept of attribute closure in the context of database management systems (DBMS), highlighting its importance in identifying candidate keys, checking functional dependencies, and normalization. It provides an example with a relation R containing attributes A, B, C, D, and E, along with their functional dependencies, and demonstrates how to derive attribute closures using rules such as reflexivity, transitivity, and union. The closure sets for individual attributes and combinations are also presented, showing the attributes that can be determined from each attribute.

Uploaded by

Sagar Giri
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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LET’S START WITH DBMS :)

Attribute closure/closure set

Attribute closure helps us for identifying candidate keys, checking for functional
dependencies, and in normalisation.

where x is an attribute or set of attribute which have all the attributes in a


X
relation which can determine X.

Ques : Consider we have a relation R with atrributes A,B,C,D,E and FD are


A-> B, B-> C ,C-> D, D-> E
1. Now according to the rule of Reflexivity all the attributes can determine theirself.
A->A, B->B , C->C , D->D, E->E
LET’S START WITH DBMS :)
Attribute closure/closure set

Ques : Consider we have a relation R with atrributes A,B,C,D,E and FD are


A-> B, B-> C ,C-> D, D-> E

1. Now according to the rule of Reflexivity all the attributes can determine theirself.
A->A, B->B , C->C , D->D, E->E

2. Now according to the rule of transivity if A determines B and B determines C, then A


can also determine C and same for all other attributes.
A->C, A-> D, A->E
B->D , B->E
C->E
LET’S START WITH DBMS :)
Attribute closure

Ques : Consider we have a relation R with atrributes A,B,C,D,E and FD are


A-> B, B-> C, C-> D, D-> E

3. Now according to the rule of UNION if as the determinant is same we can combine
dependent
For A For C For E
A-> B , A->C, A-> D, A->E , A->A C-> D, C->E , C->C E->E
A->ABCDE C->DEC

For B For D
B-> C , B->D , B->E , B->B D-> E , D->D
B->CDEB D->ED
LET’S START WITH DBMS :)
Attribute closure
Ques : Consider we have a relation R with atrributes A,B,C,D,E and FD are
A-> B, B-> C, C-> D, D-> E

4. Now lets find the closure set of attributes

A- {A,B,C,D,E}
B- {B,C,D,E}
C-{C,D,E}
D- {D,E}
E- {E}
AB - {A,B,C,D,E}

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