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Mrs Neha worked for her project , designed two operations given below and asked her students to check whether language L is closed under below operations or not:

operation1(L): {wϵ L| no proper prefix of w is a member of L}

operation2(L): {wϵ L| w is not the proper prefix of any string in L}

Which of the following is true,when students run both operation for"L".

(A) if L is regular , then it is closed under both operations.

(B) if L is regular, then it is closed under operation1 but not under operation2.

(C)  if L is regular, then it is closed under operation2 but not under operation1.

(D)  if L is regular, then it is not closed under any operation.
in Theory of Computation by Loyal (5.6k points) | 60 views
is it c?
@ Minal given answer is option A
I am not getting difference between two operations according to me they are same only!!

Suppose L = a*b

Then, Op1(L)={ b,ab,aab,aaab,....} Which is regular.

Op2(L)={b,ab,aab...} Which is also regular.

Correct me if in doing some mistake!
pls check this:-

if  string is aaab

then acc. to

operation 1:- {a,aa,aaa} should not get accepted;

so i can do it making just last state the final state!

operation2:- sigma* -{a,aa,aaa}

here sigma* is regular, a,aa,aaa are also regular, complement of regular is regular;

therefore this is closed!

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