Superset Relation

A Superset Relation is a binary set operation that ...

• See: Union Operation, Subset, Superclass, Inclusion (Boolean Algebra), Apache Superset.

---

---

References

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Subset Retrieved:2017-6-8.
  • In mathematics, especially in set theory, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment. ...

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Subset#Definitions Retrieved:2017-6-8.
  • 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 [math]\displaystyle{ A \subseteq B }[/math] ,

    :or equivalently

     :* B is a superset of (or includes) A, denoted by [math]\displaystyle{ B \supseteq A. }[/math] If A is a subset of B, but A is not equal to B (i.e. there exists at least one element of B which is not an element of A), then

     :* A is also a proper (or strict) subset of B ; this is written as [math]\displaystyle{ A \subsetneq B. }[/math] :or equivalently

     :* B is a proper superset of A ; this is written as [math]\displaystyle{ B \supsetneq A. }[/math] For any set S, the inclusion relation ⊆ is a partial order on the set [math]\displaystyle{ \mathcal{P}(S) }[/math] of all subsets of S (the power set of S) defined by [math]\displaystyle{ A \leq B \iff A \subseteq B }[/math] . We may also partially order [math]\displaystyle{ \mathcal{P}(S) }[/math] by reverse set inclusion by defining [math]\displaystyle{ A \leq B \iff B \subseteq A }[/math] .

    When quantified, A ⊆ B is represented as: ∀x{x∈A → x∈B}.

---