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In set theory, a subset is a set which has some (or all) of the elements of another set, called superset, but does not have any elements that the superset does not have. A subset which does not have all the elements of its superset is called a proper subset. We use the symbol ⊆ to say a set is a subset of another set. We can also use ⊂ if it is a proper subset. The symbols ⊃ ⊇ are opposite - they tell us the second element is a (proper) subset of the first.[1][2][3]

For example:

  • {1, 2, 3} is a proper subset of {-563, 1, 2, 3, 68}.
[math][0, 1] \subset R[/math]
[math][0, 1] \subset R_+[/math]
  • {46,189,1264} is its own subset, and is a proper subset of the set of natural numbers.
[math]\{ 46,189,1264\} \subseteq \{ 46,189,1264\}[/math]
[math]\{ 46,189,1264\} \subset N [/math]

Related pages


  1. "Comprehensive List of Set Theory Symbols" (in en-US). 2020-04-11. 
  2. Weisstein, Eric W.. "Subset" (in en). 
  3. "Introduction to Sets".