N-ary Relations and Their Applications Rosen 8.2.

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

n

domainsAAA

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n

n

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isrelation theof degree The

relation theof theare ,,, sets The

product cartesian theofsubset a isrelation An

sets be ,,Let

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NNNR

such that ),,(

triplesof consisting on relation thebe Let

Note: N is the set of natural numbers {0,1,2,3,…}

An example

}),3,2,1(,),4,2,0(),3,2,0(,),3,1,0(),2,1,0{( R

R)3,4,2(

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


)0()(such that ),,,(

tuples-4 of consisting on relation thebe Let

dcbadcbadcba

ZNZNR

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

R

R

)9,3,6,6(

)3,3,11,5(

)0,1,1,0(

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


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3.90sMathematic678543Rao

3.49sMathematic453876Goodfriend

3.49ScienceComputer 102147Chou

3.45Physics888323Adams

3.88ScienceComputer 231455Ackermann

GPADeptmetricNoName

Example from the book

Attributes: name, metric No, Dept and GPA








GPADeptmetricNoName

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








GPADeptmetricNoName

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








GPADeptmetricNoName

A composite key is a combination of attributesThat uniquely define tuples

Relational databases Operations on n-ary relations







GPADeptmetricNoName

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Projection

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2.99Stevens

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GPAName

Relational databases Operations on n-ary relationsJoin

Joins two tables/relations together, matching up on specific attributes

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TimeRoomCourseDeptLecturer

Explain the previous slide

Explain how what we do differs from what will be presented in IM2

N-ary Relations and Their Applications Rosen 8.2.

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