Let L be a language over Σ i.e., $L\subseteq Σ^∗$. Suppose L satisfies the > two conditions given below.
- L is in NP and
- for every n, there is exactly one string of length n that belongs to L. Let $L^c$ be the complement of L over $Σ^∗$.
Show that $L^c$ is also in NP.
If L is a language in NP then L is Turing decidable. So, complement of L is also Turing decidable but not necessarily in NP. To prove it is NP we have to use (ii).
I don't know how to prove it is NP using (ii).
Can you explain it in a formal way, please?