Let \(X\) be a recursive language and \(Y\) be a recursively enumerable but…

GATE · 2016 · CS · Set 1 · Computer Science & IT

Let XX be a recursive language and YY be a recursively enumerable but not recursive language. Let WW and ZZ be two languages such that Y‾\overline Y reduces to WW, and ZZ reduces to X‾\overline X (reduction means the standard many-one reduction). Which one of the following statements is TRUE?

  1. A.

    WW can be recursively enumerable and ZZ  is recursive.

  2. B.

    WW can be recursive and ZZ  is recursively enumerable.

  3. C.

    WW is not recursively enumerable and ZZ  is recursive.

  4. D.

    WW is not recursively enumerable and ZZ  is not recursive.

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