Your approach? @Kushagra गुप्ता
I was just thinking if I can get an assurity about the answer, then I can explain in detail :) as I have gone through these types of questions but not exactly this one. It is a good question.
Since designated initial state given then initial state has to be fix
If there are three states X,Y,Z and if we make X as initial state then we are not going to change it throughout the process because designated initial state given in the question and we know ⋵ is not empty language It is empty string So here we can't make X as final state because it's already initial state so that if we make X as final state then our DFA is going to accept empty string (means atleast one string ) So our DFA not able to accept empty language that's why we don't make X as the final state because by doing this our DFA can't able to accept empty language
Here one thing that we need to keep in mind is that if there is no final state then whatever transition we write DFA can't accept anything means DFA accept empty language that we want and If there is atleast one final state then our DFA can able to accept empty language only if final state is not reachable from initial state
Thank you @Kushagra गुप्ता for solving this problem
Are you sure about this ?
No final state$=729 \checkmark$
Two final state$=81 \checkmark$
For One final state, let's take $Y,$ I am getting$=189$
For One final state, let's take $Z,$ I am getting$=189$
Yes you are right Thank you:)