theory of autometa

Question

let M be a finite autometa .let M' denote the machine obtained by interchanging the final and non final state

1. L(M) U L(M') =sigma*
2. L(M) $\cap$ L(M') =$\Phi$

how many statement is true 

and answer is both are true  .

no need to read the below part of the question because that is useless

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i am sure that 1st is true 

but for 2nd take an example 

so 2nd become false but given that both are true for DFA 

where i am doing mistake  ??

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i found my mistake that is i am changing initial state to final state and vice versa

but is should be  to find the complement we have to make non final state to final state and final to non final  and no other change

now the the correct image is 

so both statement is true

Comments

 to find the complement we have to make non final state to final state and final to non final  and no other change here we can see the example

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Is this doubt still uncleared??

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no...    now it is fully clear

Answer 1

Simple DFA concept