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Inclusion (logic) In logic and mathematics, inclusion is the concept that all the contents of one object are also contained within a second object. [1] For example, if m and n are two logical matrices, then. The modern symbol for inclusion first appears in Gergonne (1816), who defines it as one idea 'containing' or being 'contained' by another ...
Inclusion map. 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. An inclusion map may also be referred to as an inclusion function, an insertion, [1] or a canonical injection. A "hooked arrow" (U+ 21AA ↪ RIGHTWARDS ARROW WITH ...
Inclusion–exclusion principle. In combinatorics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as. where A and B are two finite sets and | S | indicates the cardinality of a set S (which may be ...
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 relationship of one set being a subset of another is called inclusion (or sometimes containment).
propositional logic, Boolean algebra, first-order logic. ⊥ {\displaystyle \bot } denotes a proposition that is always false. The symbol ⊥ may also refer to perpendicular lines. The proposition. ⊥ ∧ P {\displaystyle \bot \wedge P} is always false since at least one of the two is unconditionally false. ∀.
By definition, every strict weak order is a strict partial order. The set of subsets of a given set (its power set) ordered by inclusion (see Fig. 1). Similarly, the set of sequences ordered by subsequence, and the set of strings ordered by substring. The set of natural numbers equipped with the relation of divisibility. (see Fig. 3 and Fig. 6)
Inclusion (Boolean algebra) In Boolean algebra, the inclusion relation is defined as and is the Boolean analogue to the subset relation in set theory. Inclusion is a partial order. The inclusion relation can be expressed in many ways: The inclusion relation has a natural interpretation in various Boolean algebras: in the subset algebra, the ...
In mathematics, the algebra of sets, not to be confused with the mathematical structure of an algebra of sets, defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions ...