Question: A homomorphism is a function f : ' from one alphabet to strings over another alphabet. We can extend f to operate on strings by

A homomorphism is a function f:' from one alphabet to strings over another
alphabet. We can extend f to operate on strings by defining f(w)=f(w1)f(w2)dotsf(wn),
where w=w1w2dotswk. and each wtin. We further extend f to operate on languages by
defining f(A)={f(w)|winA}, for any language A.
a. Show, by giving a formal construction, that the class of regular languages is closed
under homomorphism. In other words, given a DFA M that recognizes B and a
homomorphism f, construct a finite automaton M' that recognizes f(B). Consider the
machine M' that you constructed. Is it a DFA is every case?
b. Show, by giving an example, that the class of non-regular languages is not closed
under homomorphism.
please make the answer readable and easy to follow
A homomorphism is a function f:' from one alphabet to strings

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