Answer: (i) $P$ is a subset of $NP$

Explanation:

• $P \subseteq NP$ and it is unknown whether $P = NP$ (Clay Millennium problem).
• Every problem solvable in polytime (P) is also verifiable in polytime (NP) — just solve and check.
• Converse $NP \subseteq P$ would imply $P=NP$, unproven.
• $P$ and $NP$ are not disjoint; $P \cap NP = P$.

Venn: $P \subseteq NP$, $NP$-Complete $\subset NP$, $NP$-Hard ⊇ $NP$-Complete (some outside $NP$).

Correct choice: (i)