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Relation

Introduction to relation

The relation we are going to study here is an abstraction of relations we see in our everyday life such as those between parent and child, between car and owner, among name, social security number, address and telephone number etc. We are going to focus our attention on one key property which all the everyday relations have in common, define everything that has that property as a relation, and study properties of those relations. One of the places where relation in that sense is used is data base management systems. Along with hierarchical and network models of data, the relational model is widely used to represent data in a database. In this model the data in a database are represented as a collection of relations. Informally, each relation is like a table or a simple file. For example, consider the following table.

Employee
Name Address Home Phone
Amy Angels 35 Mediterranean Av. 224-1357
Barbara Braves 221 Atlantic Av. 301-1734
Charles Cubs 312 Baltic Av. 223-9876
Each row of this table represents a collection of data values such as name, address, and telephone number of a person. Each row is considered an instance of a relation and the table as the collection of the rows is considered a relation, which is the relation we are going to be studying in this chapter. Operations such as inserting or deleting entries to or from a table, merging two tables, finding the intersection of two tables, and searching for certain entries can be described simply and precisely as operations on relations, and known mathematical results on relations can be utilized without reinventing them. The relational model is flexible (easy to expand, easy to modify) and interface to query languages is simple. It is thus widely used today.

Definitions

Binary relation

Here we are going to define relation formally, first binary relation, then general n-ary relation. A relation in everyday life shows an association of objects of a set with objects of other sets (or the same set) such as John owns a red Mustang, Jim has a green Miata etc. The essence of relation is these associations. A collection of these individual associations is a relation, such as the ownership relation between peoples and automobiles. To represent these individual associations, a set of "related" objects, such as John and a red Mustang, can be used. However, simple sets such as {John, a red Mustang} are not sufficient here. The order of the objects must also be taken into account, because John owns a red Mustang but the red Mustang does not own John, and simple sets do not deal with orders. Thus sets with an order on its members are needed to describe a relation. Here the concept of ordered pair and, more generally, that of ordered n-tuple are going to be defined first. A relation is then defined as a set of ordered pairs or ordered n-tuples.

Definition (ordered pair):

An ordered pair is a set of a pair of objects with an order associated with them. If objects are represented by x and y, then we write an ordered pair as<x, y>or<y, x>. In general<x, y>is different from<y, x>.

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Discrete structures. OpenStax CNX. Jan 23, 2008 Download for free at http://cnx.org/content/col10513/1.1
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