[Solved]: Are two non-Turing-recognizable languages closed under union?

Problem Detail: 

If I have two languages that aren't Turing-recognizable, is the union between them always not T-recognizable? Why?

Asked By : RobotMan

Answered By : jmite

No, sometimes you can recognize their union. As an example, take a language where it and its complement are undecidable. Then their union is decided by a TM that always says yes.

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Question Source : http://cs.stackexchange.com/questions/35573