The situation when P is a superset of NP
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}