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A is a subset of B (denoted ) and, conversely, B is a superset of A (denoted ). In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B.
The notation = . may be used if is a subset of some set that is understood (say from context, or because it is clearly stated what the superset is). It is emphasized that the definition of L ∁ {\displaystyle L^{\complement }} depends on context.
A is a subset of B. B is a superset of A. An Euler diagram is a graphical representation of a collection of sets; each set is depicted as a planar region enclosed by a loop, with its elements inside. If A is a subset of B, then the region representing A is completely inside the region representing B. If two sets have no elements in common, the ...
Standard set theory symbols with their usual meanings (is a member of, equals, is a subset of, is a superset of, is a proper superset of, is a proper subset of, union, intersection, empty set) ∧ ∨ → ↔ ¬ ∀ ∃ Standard logical symbols with their usual meanings (and, or, implies, is equivalent to, not, for all, there exists) ≡
An abstract simplicial complex is a set family (consisting of finite sets) that is downward closed; that is, every subset of a set in is also in . A matroid is an abstract simplicial complex with an additional property called the augmentation property .
Horseshoe [1] (⊃, \supset in TeX) is a symbol used to represent: Material conditional in propositional logic; Superset in set theory; It was used by Whitehead and Russell in Principia Mathematica. In Unicode the symbol is encoded U+2283 ⊃ SUPERSET OF (⊃, ⊃, ⊃).
In mathematics, a subset of a given set is closed under an operation of the larger set if performing that operation on members of the subset always produces a member of that subset. For example, the natural numbers are closed under addition, but not under subtraction: 1 − 2 is not a natural number, although both 1 and 2 are.
The section "⊂ and ⊃ symbols" only mentions the symbols ⊊ and ⊋ as something some authors prefer not to use. The reference there does not mention these symbols. It would be useful to find a positive reference for authors that do prefer to use ⊊ and ⊋ for proper sub/supersets, and use ⊂ and ⊃ where the two sets may be equal.