Browse Questions

True or False: A binary operation on a set has always the identity element.

Toolbox:
• 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'