 Now, there might be special sets of properties for which the supervenience of A on B guarantees that there are B-properties that entail the A-properties—namely, property sets that are closed under the Boolean operations of complementation, infinitary conjunction, infinitary disjunction (see Kim 1984), and operations involving quantification. Closing {F} and {~F} under these operations will result in the same set, namely {F, ~F, F &amp; ~F, F v ~F…}. In both cases just above, then, the closure of B under these operations in fact contains a property that entails the A-property.