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GATE CS and IT 2016 Paper 1

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Question : 54

Total: 65

Let X be a recursive language and Y be a recursively enumerable but not recursive language.Let W and Z be two languages such that

reduces to W, and Z reduces to

(reduction means the standard many-one reduction). Which one of the following statements is TRUE?

W can be recursively enumerable and Z is recursive
W can be recursive and Z is recursively enumerable
W is not recursively enumerable and Z is recursive
W is not recursively enumerable and Z is not recursive.

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