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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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True or False: A binary operation on a set has always the identity element.

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  • An identify element 'e' is defined binary operation * meet A if $ e \in A$ and $a*e=a=e*a$ for $a\in A$
Let * on set of natural number be defined by
 
$ a *b =a-b \qquad a,b \in N$
 
Let $a-b =a$
 
$b=a-a=0$
 
$(ie) b=0 \notin N$
 
Therfore there does not exist any element 'e' in N such that $a*e=e *a =a$
 
Identify element does not exists for bianry operation *
 
The given statement is 'False'

 

 

answered Mar 6, 2013 by meena.p
 

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