#NFA to Regular Expresssion conversion using elimination of states method

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prime echo
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I don't understand the answer to question 4 ii. I need to delete state 2 first so I assumed that I need to look at all the symbols going into state 2 and out of state 2. So that would mean i need to look at Q1 -> Q2 a, Q2->Q3 b, Q2-> Q2 a, Q2 -> Q1 b. Best I got was ab + ( a a ^ kleene star b ) ^ kleene star when i try to delete state 2 first. I just get thrown off by the Q2 -> Q1 b and the Q1 loop of symbol b.

Can someone please help me with this question. I would really appreciate it. I spent quite some time trying to understand but I don't get it. (Edit: it wont let me write the kleeen star * so i wrote kleene star instead in my text).

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stable nimbusBOT
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prime echo
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wait i just realised, if i delete state 2 first, well that leaves us with states 0,1 and 3. I just need to identify i,j pairs in order to know which transitions to update and how to update? i being the incoming state and j being outgoing state. And the way I see how i can update a transition is by looking at the original nfa before removing states e.g. if i need to update T: (1,b) or (1,1) whatever way u write it, i need to look at how i can get to state 1 going through state 2?

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so it would be (1,1)' = (1,1) + (1,1) + (1,2) (2,2)* (2,1) ???? idk if this is how u solve these type of questions in general? i would appreciate if someone can refine my way of thinking on how to approach these questions and solve it.

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is this way of solving applicable to different nfas? just want clarity that's all (i realised i wrote a lot lol)

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alpine mist
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stable nimbusBOT
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@prime echo

:HelpIcon:| Help Reminder

Hello neet97, this is a friendly reminder that your help request has been inactive for more than 24 hours. If you no longer need assistance, please consider closing the thread using the +close command. This thread will be automatically closed in 3 days if it remains inactive.

prime echo
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+close

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# prime echo +close
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# stable nimbus

Thank you for your feedback! Cleanse general by deleting it has been awarded 1 helper_points. They now have 112 helper_points. They have 3 helper_points daily left for today.