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Questions about relationships between complexity classes.
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Is $NP$ "minimal", i.e. does $\Pi\notin NP$ imply $\Pi$ is $NP$-hard?
Suppose $\Pi$ is a decidable decision problem.
Does $\Pi\not \in NP$ imply $\Pi$ is $NP$-Hard?
Edit: if we assume there exists $\Pi\in coNP\setminus NP$ then we are done. Can we refute the claim …