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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 Y reduces to W , and Z reduces to X (reduction means the standard many-one reduction). Which one of the following statements is TRUE? 

(A) W can be recursively enumerable and Z is recursive.

(B) W can be recursive and Z is recursively enumerable. 

(C) W is not recursively enumerable and Z is recursive. 

(D) W is not recursively enumerable and Z is not recursive.

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1 Answer

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by (70.9k points)

(C) W is not recursively enumerable and Z is recursive. 

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