Definitions
If A and B are sets and every element of A is also an element of B, then:
-
- A is a subset of (or is included in) B, denoted by ,
- or equivalently
- B is a superset of (or includes) A, denoted by
If A is a subset of B, but A is not equal to B (i.e. there exists at least one element of B not contained in A), then
-
- A is also a proper (or strict) subset of B; this is written as
- or equivalently
- B is a proper superset of A; this is written as
For any set S, the inclusion relation ⊆ is a partial order on the set of all subsets of S (the power set of S).
Read more about this topic: Subset
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