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Which of the following are useful in proving a language to be regular?

1. Myhill-Nerode theorem
2. Pumping lemma
3. Drawing an NFA
4. Forming a regular expression

(A) All of these

(B) 1, 3 and 4 only

(C) 2, 3 and 4 only

(D) 3 and 4 only

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(B)1, 3 and 4 only

As from the given options, Myhill-Nerode theorem is useful by providing necessary and sufficient condition for proving that a language regular. Pumping lemma is often used to prove that a language is non-regular. Drawing an NFA can be useful to prove a language is regular. Forming a regular expression can also help us prove if it is a regular language

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That's a perfect explanation.
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all options are right
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No. Pumping lemma cannot say if a language is regular. If pumping lemma is violated, it can say a language is not regular. But if pumping lemma is satisfied, it doesn't mean language is regular.
• The Myhill-Nerode theorem is an important characterization of regular languages. and is is used for regular language.
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• pumping lemma is a negativity test and it is used for non regular.
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• if you drow a dfa . then the language is regular .
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• if you forming a regular expression .then the language is regular

so option 1,3,4 is right

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