Every subset of a set — including the empty set and the set itself.
The power set P(S) is the set of every possible subset of S, including the empty set ∅ and S itself. For a set of 3 elements, P(S) has 8 subsets.
Each existing subset can either include or exclude a new element — two choices per existing subset — so |P(S)| = 2^|S|. Adding one element to a set exactly doubles its power set's size.
Yes — the empty set ∅ is a subset of every set, so it's always included in P(S), along with S itself as the largest subset.