I have a question from a test that I could not pass, I could not answer the question and I am looking for help with this question
This is the question
Will be $A\in \mathbf{NP}$
Suppose that $A\notin \mathbf{coNP}$. determine which of the claims is correct:
- $\mathbf{P}=\mathbf{coNP}$
- $\mathbf{P}=\mathbf{NP}$
- $\mathbf{P}\neq \mathbf{NP}$
- $\mathbf{NP} \cap \mathbf{coNP} = \varnothing $
According to the data in the question, you need to choose the correct answer from the 4 possible answers.
I do not understand if there is any connection at all between the language A, and the answers themselves.
What I think is that A must only be in $\mathbf{NP}$ and it cannot be in $\mathbf{P}$, because it is not in $\mathbf{coNP}$, and $\mathbf{coNP}$ itself is in $\mathbf{P}$.
But I do not find an answer that can fit it, maybe 3 is correct, but it has nothing to do with the question at all, it is always true.