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Let's write formally what $L$ and $\overline{L}$ are: $$L=\{\langle M,w,b \rangle| (b=0 \wedge M(w) \mbox{ halts}) \vee (b=1 \wedge M(w) \mbox{ does not halt}) \}$$ $$\overline{L}=\{\langle M,w,b \rangle| (b=1 \vee M(w) \mbox{ does not halt}) \wedge (b=0 \vee M(w) \mbox{ halts}) \}$$ The latter is confusing, so let's rearrange it: $$\overline{L}=\{\langle ...

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