The situation when P is a superset of NP Could it be that three languages $A, B, C$ such that $A \subset B \subset C$, and $B \in P$, but $A$ and $C$ are $NP$-complete?
Let $L$ be any NP-complete language over $\Sigma = \{0,1\}$, and take
\begin{align}
A &amp;= \{ 0x : x \in L \} \\
B &amp;= 0\Sigma^* \\
C &amp;= 0\Sigma^* \cup \{ 1x : x \in L \}
\end{align}