Showing that 
and M are isomorphic
and M are isomorphic
To show that and M are isomorphic we have to define a bijection 
that satisfies all the three conditions given in the definition of DFA isomorphism.
- Recall that the states of are
where 
are the representatives of each k equivalence classes of 
. - Let us define as follows
- f is onto since
That is, f maps state 
of to the state in M which can be arrived at processing the string 
from the start state of M. we know that 
. Hence f is well-defined.
continued....