17

They are separate (assuming $P \ne NP$). Consider the following property $P(x)$: $x$ is a $2n$-bit string, where either the first $n$ bits are not all zeros, or the last $n$ bits are a yes-instance of 3SAT. It's clear that testing whether $x$ satisfies $P$ is NP-hard, yet almost all strings satisfy it: the density $\to 1$ as $n \to \infty$.


Only top voted, non community-wiki answers of a minimum length are eligible