Set Theory
Subsets
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
- The symbol ⊆ (or ⊇, reversed) is used do denote the subset/superset relationship:
if A = {r, s, t},
and B = {r, s, t, u, v}, and
A ⊆ B, and
B ⊇ A
- The symbol ⊂ (or ⊃, reversed) is used do denote a proper subset/superset relationship:
if A = {r, s, t},
and B = {r, s, t, u, v}, and
A ⊂ B, and
B ⊃ A
- The symbol ⊄ is used do denote "not a subset":
if A = {r, s, t},
and B = {r, s, u, v}, and
A ⊄ B, and
