Testbook

Question

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. Suppose an operation is defined on a regular language A. In which of the following options, the class of the regular language is closed? The answer given is a.

1. NOPREFIX(A) = {w ∈ A | no proper prefix of w is a member of A}
2. EXTEND(A) = {w ∈ A | w is the proper prefix of any string in A}
3. PREFIX(A) = {w ∈ A | proper prefix of w is a member of A}
4. None of the above

Comments

i hope all are closed under RL,

i am not getting why option a only correct, can you post their solution?

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all are regular for sure.

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@Shaik Masthan, @aambazinga Could you please elaborate how they all are regular?