Terms

subset, n.
(math) The set A is a subset of set B iff every member of A is also a member of B.
proper subset, n.
(math) The set A is a proper subset of set B iff A is a subset of B, but B is not a subset of A.
proper superset, n.
(math) The set A is a proper superset of set B iff A is a superset of B, but B is not a superset of A.
set equality, n.
(math) Two sets A and B are equal iff A is a subset of B, and B is a subset of A.
superset, n.
(math) The set A is a superset of set B iff every member of B is also a member of A.

Symbols

is a proper subset of
is a subset of
is a proper superset of
is a superset of
is not a subset of

Notation