Prove that for each n > 0, a language Bn exists where a. B n is recognizable

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Prove that for each n > 0, a language Bn exists where

a. Bn is recognizable by an NFA that has n states, and

b. if Bn = A1 ∪ · · · ∪ Ak, for regular languages Ai, then at least one of the Ai requires a DFA with exponentially many states.

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