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

Let $$ < M > $$ be the encoding of a Turing machine as a string over $$\sum { = \left\{ {0,1} \right\}.} $$
Let $$L = \left\{ { < M > \left| M \right.} \right.$$ is a Turing machine that accepts a string of length $$\left. {2014} \right\}.$$ Then, $$L$$ is

Let $$L$$ be a language and $$\overline L $$ be its complement. Which one of the following is NOT a viable possibility?

If $$L$$ and $$\overline L $$ are recursively enumerable then $$L$$ is