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   Abhiseck Paira :gnu: :gnuhurd: (redstarfish@social.linux.pizza)'s status on Thursday, 27-Mar-2025 01:50:33 JST Abhiseck Paira :gnu: :gnuhurd:

   in reply to

   @cnx

   I've found a argument to generate counter examples that show it's not necessary that A = B.

   Let C be a language that's union of two languages A1 and A2. Now we construct a DFA M that recognizes the union language.

   We'll see that M also recognizes A1 and A2 separately, yet clearly A1 is not necessarily equal to C (A1 is a subset of C).

   Similarly, A1 is not equal to A2.

   CC: @shakil_tcs