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Question: let be an alphabet for a word w ...

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Let Σ be an alphabet. For a word w = a1 ···an and a (total) function h from Σ to Σ, we use h(w) to denote h(a1)···h(an). For a language L over the alphabet, we use h(L) to denote {h(w) : wL}. Prove that (1). If L is a regular language, then so is h(L). (2). There is a non-regular language L such that h(L) is a regular language for some h.

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