computer science - Induction on String? (automata related) -

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honestly, know mathematical induction follow:

1. prove p(0) - base step 2. n ≥ 1, prove (p(n − 1) -> p(n)) - inductive step

and here image of induction problem struggling (please click)

i trying solve problem above image, can't. new kind of thing, have no idea , cannot infer little knowledge.

i don't know how start , don't know how can apply little knowledge described above problem.

thank if can me on above problem careful explanation..

as hint, let p(k) statement "any language k strings regular." using induction idea, you'd need following:

  1. prove language 0 strings in regular. can language no strings in it? can build dfa, nfa, or regex such language?

  2. assume language n-1 strings regular, prove language n strings regular. if language has n strings in it, can split language n-1 strings in , language 1 string in it. can first language? if had regex it, adapt regex language 1 more string in it?


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