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 $=$

$\{\backslash$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.