blanketglossary

Boolean algebra

Definition

In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and negation (not) denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations.

Related concepts

AND gate A Symbolic Analysis of Relay and Switching Circuits Abstract algebra Abstract logic Ackermann set theory Aleph number Algebra Algebra of sets Algebraic logic Algebraic semantics (mathematical logic)Algebraic structure Algorithm Alphabet (formal languages)An Investigation of the Laws of Thought Application-specific integrated circuit Argument Arity Assembly language Asynchronous circuit Atomic formula Atomic model (mathematical logic)Atomic sentence Automata theory Automated theorem proving Automorphism Axiom Axiom of choice Axiom schema Axiomatic system Axiomatization Axiomatization of Boolean algebras Axioms Banach–Tarski paradox Bell System Technical Journal Bijection Binary decision diagram Binary number Binary operation Binary operator Bit Bit array Bit blit Bitwise Bocheński, Józef Maria Boolean-valued semantics Boolean algebra (disambiguation)Boolean algebra (structure)Boolean algebras canonically defined Boolean circuit Boolean differential calculus Boolean function Boolean polynomial Boolean prime ideal theorem Boolean satisfiability problem Boolean variable Booleo Branden Fitelson CRC Press Cambridge University Press Cambridge and Dublin Mathematical Journal Cantor's diagonal argument Cantor's paradox Cantor's theorem Cantor algebra Capacitor Cardinality Carry (arithmetic)Cartesian product Categorical theory Category (mathematics)Category of sets Category theory Characteristica universalis Charles Sanders Peirce Church encoding Church–Turing thesis Circuit complexity Circuit diagram Circuit minimization for Boolean functions Class (set theory)Classical logic Claude Shannon Codomain Cofinite Combinational logic Compactness theorem Complement (set theory)Complemented lattice Complete theory Complex programmable logic device Computability theory Computable function Computable set Computably enumerable set Computer Computer aided design Computer architecture Computer displays Computer hardware Concrete category Conjunction/disjunction duality Conservative extension Consistency Constructible universe Construction of the real numbers Constructive set theory Continuum hypothesis Countable set Courier Dover Publications De Morgan's law De Morgan's laws De Morgan duality Decidability (logic)Decision problem Deductive system Diagram (mathematical logic)Digital audio Digital cinematography Digital electronics Digital logic Digital photography Digital radio Digital signal Digital signal (signal processing)Digital signal processing Digital television Digital video Disjunction Distributive lattice Domain of a function Edward Vermilye Huntington Electronic circuit Electronic component Electronic design automation Electronic literature Electronics design Element (mathematics)Elementary algebra Elementary diagram Elementary equivalence Elementary function arithmetic Elsevier Emitter-coupled logic Empty set Entailment Enumeration Equiconsistency Equivalence relation Erasable programmable logic device Ernst Schröder (mathematician)Euclid's Elements Euclidean geometry Existential quantification Expression (mathematics)Extension by definitions Extension by new constant and function names Extensionality False premise Field-programmable gate array Field-programmable object array Field (mathematics)Field of sets Finitary relation Finite-state machine Finite-valued logic Finite model theory Finite set First-order logic Fixed-point logic Flip-flop (electronics)Forcing (mathematics)Formal equivalence checking Formal grammar Formal language Formal proof Formal semantics (logic)Formal system Formal verification Formation rule Foundations of geometry Foundations of mathematics Free logic Free variables and bound variables Function (mathematics)Function composition Functional predicate Fuzzy logic Fuzzy set GF(2)Gate equivalent General set theory Generic Array Logic George Boole Google Gottfried Wilhelm Leibniz Greatest common divisor Grothendieck universe Ground expression Ground formula Group (mathematics)Group action (mathematics)Group theory Gödel's completeness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Hardware acceleration Hardware description language Harvard University Press Henry M. Sheffer Hereditary set Heyting algebra Hierarchical state machine High-level synthesis Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic Hybrid integrated circuit I Ching Idempotence Identity (mathematics)Image (mathematics)Inaccessible cardinal Indefinite article Independence (mathematical logic)Index set Indexed family Indicator function Inductor Inference Infinite-valued logic Infinite set Information theory Inhabited set Injective function Integer Integrated circuit Internet Encyclopedia of Philosophy Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Intuitionistic logic Inverter (logic gate)Isomorphic Isomorphism Jean-Yves Girard John Etchemendy John Venn Jon Barwise Journal of Automated Reasoning Klein four-group Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Lambda calculus Large cardinal Larry Wos Least common multiple Lemma (mathematics)Lindström's theorem List of Boolean algebra topics List of Hilbert systems List of axioms List of first-order theories List of formal systems List of mathematical theories List of set identities and relations List of statements independent of ZFC Logic Logic design Logic gate Logic gates Logic in computer science Logic optimization Logic synthesis Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical operation Logical operator Logical system Logical truth Logicism Löwenheim–Skolem theorem M. H. Stone Machine code Macrocell array Magnetic storage Many-valued logic Map (mathematics)Mask (computing)Material conditional Mathematical logic Mathematical object Mathematical structure Mathematics Memory cell (computing)Metalanguage Metastability (electronics)Minimal axioms for Boolean algebra Mixed-signal integrated circuit Model (logic)Model complete theory Model of computation Model theory Modular arithmetic Monadic predicate calculus Monadic second-order logic Morse–Kelley set theory Multi-valued logic NP-complete NP (complexity)Naive set theory Natural deduction Negation New Foundations Non-Euclidean geometry Non-logical symbol Non-standard model Non-standard model of arithmetic North Holland Number OR gate Open formula Operation (mathematics)Ordinal analysis Ordinal number Oxford University Press P (complexity)P versus NP problem Paper tape Paradoxes of set theory Partially ordered set Partition of a set Paul Richard Halmos Peano axioms Philosophy of mathematics Pixels Place and route Placement (electronic design automation)Power set Predicate (mathematical logic)Predicate logic Predicate variable Prime model Primitive recursive arithmetic Primitive recursive function Princeton University Press Principia Mathematica Printed circuit board Printed electronics Probabilistic logic Programmable Array Logic Programmable logic array Programmable logic device Programming language Programming languages Prometheus Books Proof of impossibility Proof theory Proposition Propositional calculus Propositional formula Propositional logic Propositional variable Punched card Quantifier (logic)Quantifier rank Raster graphics Real number Recursion Recursive set Register-transfer level Relation (mathematics)Relation algebra Relevance logic Resistor Reuben Louis Goodstein Reverse mathematics Ring (mathematics)Robinson arithmetic Roman Sikorski Routing (electronic design automation)Rule of inference Runt pulse Russell's paradox Satisfiability Saturated model Schröder–Bernstein theorem Second-order arithmetic Second-order logic Self-verifying theories Semantic theory of truth Semantics of logic Sentence (mathematical logic)Sequence Sequent Sequent calculus Sequential logic Set (mathematics)Set theory Sheffer stroke Sic Signature (logic)Singleton (mathematics)Skolem arithmetic Solid modeling Soundness Spectrum of a sentence Spectrum of a theory Springer-Verlag Springer Science+Business Media Square-free integer Square of opposition Stanford Encyclopedia of Philosophy Statistics Stone's representation theorem for Boolean algebras Strength (mathematical logic)String (formal languages)Structure (mathematical logic)Subset Substitution (logic)Substructure (mathematics)Supertask Surjective function Switching circuit Switching circuit theory Syllogism Symbol (formal)Synchronous circuit 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)Telephony Tensor Processing Unit Term (logic)Term logic The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science Theorem Theoretical computer science Theories of truth Theory (mathematical logic)Three-dimensional integrated circuit Three-valued logic Time complexity Timeline of mathematical logic Transaction-level modeling Transactions of the American Mathematical Society Transfer principle Transistor Transitive set True arithmetic Truth assignment Truth predicate Truth table Truth tables Truth value Turing machine Two-element Boolean algebra Two-valued logic Type (model theory)Type theory Ultrafilter (set theory)Ultraproduct Unary operator Uncountable Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Unit interval Universal quantification Universal set Universe (mathematics)Urelement Validity (logic)Variable (mathematics)Vector logic Venn diagram Very-large-scale integration Video cards Von Neumann universe Von Neumann–Bernays–Gödel set theory Voxel Walter Gottschalk Well-formed formula William McCune William Stanley Jevons Word (data type)Zermelo–Fraenkel set theory Łukasiewicz logic

145 concepts already in your glossary