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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.
Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})
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 } ).
A built-in function, or builtin function, or intrinsic function, is a function for which the compiler generates code at compile time or provides in a way other than for other functions. [23] A built-in function does not need to be defined like other functions since it is built in to the programming language. [24]
Each such rule can be read as an implication: … meaning "If each is true, then is true". Logic programs compute the set of facts that are implied by their rules. Many implementations of Datalog, Prolog, and related languages add procedural features such as Prolog's cut operator or extra-logical features such as a foreign function interface.
Although the type of a logical disjunction expression is Boolean in most languages (and thus can only have the value true or false), in some languages (such as Python and JavaScript), the logical disjunction operator returns one of its operands: the first operand if it evaluates to a true value, and the second operand otherwise.
[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]