Recall that string $x$ is a $\text{prefix}$ of string $y$ if a string $z$ exists where $xz = y,$ and that $x$ is a $\text{proper prefix}$ of $y$ if in addition $x\neq y.$ 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$.$
- $\text{NOPREFIX(A) ={w ∈ A|no proper prefix of w is a member of A}.}$
- $\text{NOEXTEND(A) = {w ∈ A| w is not the proper prefix of any string in A}.}$
