Relation and Their Properties

8/6/2019 Relation and Their Properties

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Relation and their Properties


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Relation:

Relation gives the idea of the association between

elements.

Ex 1: Greater than, Less than , equality

Example 2:If A and B are any two sets then any subset of

A x B defines relation from A to B is denoted by R.

Let A={1,3} and B={5,6,7}

A X B={(1,5),(1,6),(1,7),(3,5),(3,6),(3,7)}

By definition {(1,5)}C A X B is a relation.

So we will have 26

relations from A to Bi.e If and then there will be 2mn relations from

A to B.


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Domain and Range of the relation:

Domain:

If R is the relation defined from A to B then domainof R is the set of elements of A which are related to

the elements of B and denoted by Dom(R)

Let A={1,2,3} and B={5,6}

R={(1,5),(1,6),(2,5)}

Here Dom(R) ={1,2}

Range:

The set of elements of B which are related to theelements of A and is denoted by Range( R)

Range (R )={5,6}


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Types of Relation:

Onto relation(Surjective relation):

The relation R defined from A to B is called ontorelation if Dom(R )=A and Ran( R )=B


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Into relation(Injective Relation)

The relation R defined from A to B is called into

relation if every element of A connected to theelement of B but there exist at least one element

of B which is not connected to elements of A.


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One one and into relation:

The relation R defined from A to B is called one to one

and into relation if R is into relation and differentelement of A connects to different element of B.


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One to one and onto relation(Bijective Relation)

The relation R defined from A to B is called one to

one and onto if R is one to one and also onto.


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Binary Relation:

If R is the relation defined on a set A then R is calledbinary relation.

Properties of binary relation:

A relation R defined on a set A is called reflexiverelation if each member of A connected to itself. If

Example :

1.If A={1,2,3} then the relation R={(1,1),(2,2),(3,3)} is

a reflexive relation.

2.if A={a,b,c} then the relation R={(a,a),(b,b)} is not reflexive

because (c,c) not element of R.


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Symmetric Relation:

The relation R defined on a set A is called symmetric

relation if for every x,y E A such thatIf A={1,2,3}

Then the relation given by R={(1,2),(2,1),(3,2),(2,3)}

is a symmetric relation


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Relation and Their Properties

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