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Let A and B be disjoint languages, that is, A ∩ B = ∅. We say that the language C separates the languages A and B if A ⊆ C and B ⊆ C(Complement). We say that A and B are recursively separable if there is a decidable language C that separates A and B. Suppose that A(Complement) and B(Complement) are recognizable. Prove that A and B are recursively separable.
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