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. For

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 =
{\lambda ,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.

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