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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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