Automata and Computability NOPREFIX

Say 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.

a. 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}

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