 It should therefore come as no surprise that the cases that served as counterexamples to the claim that supervenience is a form of entailment also serve as counterexamples to the equivalence of the possible worlds and modal operator formulations of supervenience. Being F strongly supervenes on being not-F, but fails to even weakly supervenem on it. {P &amp; Q} strongly supervenes on {P, Q}, but fails to even weakly supervenem on it. The possible world versions of weak and strong supervenience are weaker than the corresponding modal operator versions. The latter go beyond the basic idea that there cannot be an A-difference without a B-difference. Again, though, the modal operator versions are equivalent to the possible worlds versions if the base set B is closed under Boolean operations, and operations involving quantification.