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For instance, had been declared as a subset of , with the sets and not necessarily related to each other in any way, then would likely mean instead of . If it is needed then unless indicated otherwise, it should be assumed that X {\displaystyle X} denotes the universe set , which means that all sets that are used in the formula are subsets of X ...
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) ≡
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.
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 (⊃, ⊃, ⊃).
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 ...
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.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
is a subset of , and is a superset of .. In mathematics, if is a subset of , then the inclusion map is the function that sends each element of to , treated as an element of ::, =.