Define Languages $${L_0}$$ and $${L_1}$$ as follows
$${L_0} = \left\{ { < M,\,w,\,0 > \left| {M\,\,} \right.} \right.$$ halts on $$\left. w \right\}$$
$${L_1} = \left\{ { < M,w,1 > \left| M \right.} \right.$$ does not halts on $$\left. w \right\}$$

Here $$ < M,\,w,\,i > $$ is a triplet, whose first component, $$M$$ is an encoding of a Turing Machine, second component, $$w$$, is a string, and third component, $$t,$$ is a bit.
Let $$L = {L_0} \cup {L_1}.$$ Which of the following is true?