n-ary relations and their applications rosen 8.2
TRANSCRIPT
n-ary Relations and Their Applications
Rosen 8.2
n-ary relations
We can have relation between more than just 2 sets
A binary relation involves 2 sets and can be described by a set of pairsA ternary relation involves 3 sets and can be described by a set of triples…
An n-ary relation involves n sets and can be described by a set of n-tuples
Relations are used to represent computer databases
Also used to represent constraints!
n-ary relations n-ary Relations
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Note: N is the set of natural numbers {0,1,2,3,…}
An example
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Note: R could be considered as an extensional representation of the ternary relation a<b<c, assuming domains are finite and really quite small
The relation has degree 3
The domains of the relation are the set of natural numbers
n-ary relations n-ary Relations
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tuples-4 of consisting on relation thebe Let
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Note: N is the set of natural numbers {0,1,2,3,…} Z is the set of integers {…,-2,-1,0,1,2,…}
An example
Note: R could be considered as an extensional representation of the ternary relation a<b<c, assuming domains are finite and really quite small
The relation has degree 4R
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Relational databases
Database is made up of records.Typical operations on a database are
• find records that satisfy a given criteria• delete records• add records• update records
Some everyday databases• student records• health records• tax information• telephone directories• banking records• …
Databases may be represented using the relational model
Relational databases The relational data model
Database made up of records, they are n-tuples, made up of fields
Student record might look as follows
(name,metricNo,faculty,gpa)
(Jones,200401986,Arts,4.9)(Lee,200408972,Science,3.6)(Kuhns,200501728,Humanities,5.0)(Moore,200308327,Science,5.5)
relations (in relDB) also called tables
gpa is an attribute
Relational databases The relational data model
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Example from the book
Attributes: name, metric No, Dept and GPA
Relational databases The relational data model
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primary key:An attribute/domain/column is a primary key whenthe value of this attribute uniquely defines tuplesi.e. no two tuples have the same value for that attribute
Name cannot be a primary key, neither can Dept or GPSmetricNo is a primary key
Relational databases The relational data model
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The current collection of n-tuples (records) in the relation (table)is called the extension of the relation
The permanent aspects of the relation (table) such as the attribute namesis called the intention of the relation
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A composite key is a combination of attributesThat uniquely define tuples
Relational databases Operations on n-ary relations
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Relational databases Operations on n-ary relationsJoin
Joins two tables/relations together, matching up on specific attributes
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Explain the previous slide
Explain how what we do differs from what will be presented in IM2