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

###### Question details

Let Σ be an alphabet. For a word *w* =
*a*_{1} ···*a _{n}* and a (total)
function

*h*from Σ to Σ, we use

*h*(

*w*) to denote

*h*(

*a*

_{1})···

*h*(

*a*). For a language

_{n}*L*over the alphabet, we use

*h*(

*L*) to denote {

*h*(

*w*) :

*w*∈

*L*}. 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*.