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In constructive mathematics, "not empty" and "inhabited" are not equivalent: every inhabited set is not empty but the converse is not always guaranteed; that is, in constructive mathematics, a set that is not empty (where by definition, "is empty" means that the statement () is true) might not have an inhabitant (which is an such that ).
The multiple subset sum problem is an optimization problem in computer science and operations research. It is a generalization of the subset sum problem . The input to the problem is a multiset S {\displaystyle S} of n integers and a positive integer m representing the number of subsets.
In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or — in philosophical logic — a cluster concept. [1] As a normal form, it is useful in automated theorem proving.
A logical formula is considered to be in CNF if it is a conjunction of one or more disjunctions of one or more literals. As in disjunctive normal form (DNF), the only propositional operators in CNF are or ( ∨ {\displaystyle \vee } ), and ( ∧ {\displaystyle \wedge } ), and not ( ¬ {\displaystyle \neg } ).
Logic programming is a programming, database and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical form, representing knowledge about some problem domain. Computation is performed by applying logical reasoning to that knowledge, to solve problems in the domain.
[1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. [5] A Boolean function takes the form : {,} {,}, where {,} is known as the Boolean domain and is a non ...
The wedge sum in topology; The V sign, a symbol representing peace among other things; The vertically reflected symbol, ∧, is a wedge, and often denotes related or dual operators. The ∨ symbol was introduced by Russell and Whitehead in Principia Mathematica, where they called it the Logical Sum or Disjunctive Function. [1]
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.