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Boolean function

Definition

In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set. Alternative names are switching function, used especially in older computer science literature, and truth function, used in logic. Boolean functions are the subject of Boolean algebra and switching theory.

Related concepts

AND gate Abstract logic Ackermann set theory Aleph number Algebra of sets Algebraic function Algebraic logic Algebraic normal form Alphabet (formal languages)Analysis of Boolean functions Analytic function And-inverter graph Argument Argument of a function Arity Atomic formula Atomic model (mathematical logic)Atomic sentence Autocorrelation Automata theory Automated theorem proving Axiom Axiom of choice Axiom schema Axiomatic system Axiomatization of Boolean algebras Balanced Boolean function Banach–Tarski paradox Bent function Bernoulli distribution Bijection Binary decision diagram Binary function Binary operation Binary relation Blake canonical form Boole's expansion theorem Boolean-valued function Boolean algebra Boolean algebras canonically defined Boolean circuit Boolean derivative Boolean domain Butterfly diagram Canonical normal form Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinality Cartesian product Categorical theory Category (mathematics)Category of sets Category theory Church encoding Church–Turing thesis Circuit (computer science)Circuit complexity Class (set theory)Classical logic Codomain Compactness theorem Complement (set theory)Complete theory Complex-valued function Computability theory Computable function Computable set Computably enumerable set Computational complexity theory Computer science Concrete category Conjunctive normal form Conservative extension Consistency Constant function Constructible universe Construction of the real numbers Constructive set theory Continuous function Continuum hypothesis Converse (logic)Converse nonimplication Cooperative game theory Correlation immunity Countable set Cryptography Decidability (logic)Decision problem Decision tree model Deductive system Diagram (mathematical logic)Differential cryptanalysis Digital computer Disjunctive normal form Domain of a function Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Empty set Encyclopedia of Mathematics Enumeration Equiconsistency Equivalence relation Euclid's Elements Euclidean geometry European Mathematical Society Evasive Boolean function Exclusive or Existential quantification Expression (mathematics)Extension by definitions Extension by new constant and function names Extensionality Fast Fourier transform Finitary relation Finite-valued logic Finite model theory Finite set First-order logic Fixed-point logic Forcing (mathematics)Formal grammar Formal language Formal proof Formal semantics (logic)Formal system Formation rule Foundations of geometry Foundations of mathematics Fourier transform Free logic Free variables and bound variables Function (mathematics)Function composition Function of a complex variable Function of a real variable Function of several complex variables Function of several real variables Function space Functional completeness Functional predicate Functor Fuzzy logic Fuzzy set General set theory Grothendieck universe Ground expression Ground formula Gödel's completeness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Hamming weight Harmonic Hereditary set Higher-order function Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic History of the function concept Hypercube Identity function Image (mathematics)Implicit function Inaccessible cardinal Independence (mathematical logic)Indicator function Inference Infinite-valued logic Infinite set Information theory Inhabited set Injective function Integer-valued function Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Inverse function Inverter (logic gate)Involution (mathematics)Isomorphism Karnaugh map Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Lagrange polynomial Lambda calculus Large cardinal Lemma (mathematics)Lindström's theorem Linear cryptanalysis Linear map Linearity List of Boolean algebra topics List of Hilbert systems List of axioms List of first-order theories List of formal systems List of mathematical functions List of mathematical theories List of set identities and relations List of statements independent of ZFC Logic Logic gate Logical NOR Logical biconditional Logical complement Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical truth Logicism Löwenheim–Skolem theorem Majority function Many-valued logic Map (mathematics)Material conditional Material nonimplication Mathematical logic Mathematical object Mathematics Maxterms Measurable function Metalanguage Minimal axioms for Boolean algebra Minimization of Boolean functions Minterms Model complete theory Model theory Modular arithmetic Monadic predicate calculus Monadic second-order logic Monomial Monotonic function Morphism Morse–Kelley set theory Multilinear polynomial Multivalued function Möbius transform NAND gate NIMPLY gate NOR gate NP (complexity)Naive set theory Natural deduction Negation Negation normal form New Foundations Non-Euclidean geometry Non-logical symbol Non-standard model Non-standard model of arithmetic OR gate Open formula Operation (mathematics)Ordered pair Ordinal analysis Ordinal number P (complexity)P versus NP problem Paradoxes of set theory Parity function Partial function Partially ordered set Partition of a set Peano axioms Peter L. Hammer Philosophy of logic Philosophy of mathematics Piling-up lemma Polynomial Power set Predicate (mathematical logic)Predicate logic Predicate variable Prime implicant Prime model Primitive recursive arithmetic Primitive recursive function Principia Mathematica Programming language Proof of impossibility Proof theory Proposition Propositional calculus Propositional directed acyclic graph Propositional formula Propositional variable Pseudo-Boolean function Quantifier (logic)Quantifier rank Quine–McCluskey algorithm Rational function Read-once function Real-valued function Real number Recursion Recursive set Reed–Muller expansion Relation (mathematics)Restriction (mathematics)Reverse mathematics Robinson arithmetic Rule of inference Russell's paradox S-box Satisfiability Saturated model Schröder–Bernstein theorem Scope (logic)Second-order arithmetic Second-order logic Self-verifying theories Semantic theory of truth Semantics of logic Sentence (mathematical logic)Sequence Sequent calculus Set-valued function Set (mathematics)Set theory Shannon expansion Sheffer stroke Signature (logic)Signed set Singleton (mathematics)Skolem arithmetic Smooth function Social choice theory Soundness Spectrum of a sentence Spectrum of a theory Square of opposition Strength (mathematical logic)String (formal languages)Structure (mathematical logic)Substitution (logic)Substitution box Substructure (mathematics)Supertask Surjective function Switching theory Syllogism Symbol (formal)Symmetric Boolean function Symmetric key algorithm Syntax (logic)T-schema Tarski's axiomatization of the reals Tarski's axioms Tarski's theory of truth Tarski's undefinability theorem Tarski–Grothendieck set theory Tautology (logic)Term (logic)Term logic Theorem Theories of truth Theory (mathematical logic)Three-valued logic Timeline of mathematical logic Transfer principle Transitive set True arithmetic Truth function Truth predicate Truth table Truth value Turing machine Type (model theory)Type theory Ultrafilter (set theory)Ultraproduct Unate function Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Universal quantification Universal set Universe (mathematics)Urelement Validity (logic)Variable (mathematics)Venn diagram Von Neumann universe Von Neumann–Bernays–Gödel set theory Walsh function Walsh transform Well-formed formula Wiener–Khinchin theorem XNOR gate XOR gate Zermelo–Fraenkel set theory Zhegalkin polynomial

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