[a set/sets] [an element/elements of x]
[x is in/from y @ x is an element of y]
[x belongs/belong to y @ x is in y]
[a subset/subsets of x] [x is empty]

Definition. Let S be a set.
A subset of S is a set with no elements not in S.

Definition. Let S be a set.
S is empty iff S has no elements.

Axiom. There exists an empty set.

Proposition. Let S be a set.
S is a subset of every set iff S is empty.

