Question: Let extending by 0 be an operation that takes a language and appends a 0 to the end of every string in the language.

Let "extending by 0" be an operation that takes a language and appends a 0 to the end of every string in the language. For example, if L={,01,010,1111}, then extending L by 0 would yield {0,010,0100,11110}. Describe how to construct a DFA that could be used to prove that regular languages are closed under extending by 0.
You do not have to prove that your DFA accepts then "extension by 0" language, but your solution should be still valid for infinite languages.
 Let "extending by 0" be an operation that takes a language

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