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Please help in this question i think B and C also true

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Okk Before make answer, Let's carefully observer the question. Here we can see, given machine is DFA(M) .

Definition: So we have to know the definition of DFA for a particular language, which is states that language L must contain those strings which is accepted by machine M and also does not contain those strings which is reject by the machine M .

So here in the given DFA machine M , we can observe which actually string accepted and rejected by machine are following.

Note: Always start with small Strings to large possible strings.

Accepted strings: { 00, 000, 0000, 0000, ........, 001, 010, 100, 1000, 0100, 0010, 10000, ............}

Rejected Strings: { 010101, 100011, 001010, 01010,..........} Here many strings are possible I am writing some for options elimination purpose.

Now check options.

Option (A): Here more than 1's possible while our calculated accepted strings (above) set contains single 1. [FALSE].

Option (B): Every string start with 01, 00, 10. Means after 01 or 00 or 10 you can take any number of 1's which is not the part of accepted strings set. So [FALSE].

Option (C): doesn't contain the '11' as substrings, here this language does not saying that 101 strings doesn't accept ( it definitely accepted by option C language) since 101 does not accepted by accepted strings set. [FALSE].

Options (D): This is true because it full fill our requirements regarding given machine M. [TRUE].

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