Subset Relation

A Subset Relation is a Binary Set Relation between Sets (X₁,X₂) that is True If ∀x∈X₁: x∈X₂.

• AKA: SubsetOf, Subset Operation, Subset, Inclusion Relation, ⊆.
• Example(s):
  • {} ⊆ {1, 2, 3}.
  • {1, 2, 3} ⊆ {1, 2, 3}.
  • {1, 2} ⊆ {1, 2, 3}, also a Proper Subset Relation(⊂)
• Counter-Example(s):
  • {A} ⊄ {1, 2, 3}, a Not Subset Relation.
• See: Subclass, Mathematical Symbol, Empty Set.

References

• http://wordnet.princeton.edu/perl/webwn
  • a set whose members are members of another set; a set contained within another set
• (Wikipedia, 2009) http://en.wikipedia.org/wiki/Subset
  • In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. Notice that A and B may coincide. The relationship of one set being a subset of another is called inclusion.
• http://en.wiktionary.org/wiki/subset
  • Of a given set, a set all the elements of which are in the given set; A group of things or people, all of which are in a specified larger group