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Prove that there exists a decidable language

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Let Σ = {0, 1}, and A, B ⊆ Σ∗ recognizable languages such that A ∪ B = Σ∗. Prove that there exists a decidable language C ⊆ Σ∗ such that A ∩ B ⊆ C and A ∩ B ⊆ C.

Reference no: EM131549334

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