Question: Let L be any language. Define even (w) as the string obtained by extracting from w the letters in even-numbered positions; that is, if w

Let L be any language. Define even (w) as the string obtained by extracting from w the letters in even-numbered positions; that is, if w = a1a2a3a4..., then even (w) = a2a4.... Corresponding to this, we can define a language even (L) = {even (w) : w L}. Prove that if L is regular, so is even (L)

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