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.