What does "If P1 is reduced to P2, then P2 is at least as hard as P1" mean?
Interpretation (i) is correct: &quot;$A$ is at least as hard as $B$&quot; means that $A$ is as hard as or strictly harder than $B$. (Think about numbers: &quot;$a$ is at least as big as $b$&quot; means &quot;$a=b$ or $a&gt;b$.&quot;)
Note that not only does &quot;$A$ is at least as hard as $B$&quot; rule out $A$ being strictly weaker than $B$, it also rules out $A$ and $B$ being of incomparable complexity. Complexity isn't a linear order; we can find problems such that neither helps us solve the other.