Recall that string x is a prefix of string y if a string z exists where xz = y, and that x is a proper prefix of y if in addition x ≠ y. In each of the following parts, we define an operation on a language A. Show that the class of regular languages is closed under that operation.

^Aa. NOPREFIX(A) = {w ∈ A| no proper prefix of w is a member of A}.

b. NOEXTEND(A) = {w ∈ A|w is not the proper prefix of any string in A}.