Linked from

The 80 pages that link to Boolean algebra, each with the reason it gives.

• SetRelated: Set union, intersection, and complement obey Boolean algebra's characteristic laws.

• Gottfried Wilhelm LeibnizRelated: Leibniz's project of symbolic reasoning anticipated the mathematical treatment of logic.

• Claude ShannonNarrower topic: Shannon showed that Boolean algebra describes the behavior of relay and switching circuits.

• Propositional logicRelated: Its operations provide an algebraic account of propositional connectives and equivalences.

• Power setRelated: A power set forms a Boolean algebra under union, intersection, and complement.

• Classical logicRelated: It gives classical propositional logic an algebraic representation.

• SubsetRelated: Subsets of a fixed set form a Boolean algebra under intersection, union, and complement.

• NegationRelated: Its complement operation gives an algebraic account of negation.

• Aristotelian logicCompared with: Its algebraic treatment offers a later alternative to Aristotle’s term-based method.

• Binary numeral systemRelated: Its two-valued logic maps naturally to binary states in computing.

• MultiplicationCompared with: Boolean conjunction acts like multiplication on truth values, but follows a different algebraic setting.

• Logic gateNarrower topic: Its operations define the functions that logic gates implement.

• BitRelated: Its operations provide the logic for combining and transforming binary values.

• Computer scienceRelated: Its logic underlies digital circuits, program conditions, and formal reasoning.

• Field-programmable gate arrayNarrower topic: FPGA logic implements Boolean functions using configurable hardware.

• Logical connectiveRelated: Its operations provide an algebraic treatment of truth-functional connectives.

• Truth valueRelated: Its two-element form represents false and true as algebraic values.

• Fuzzy logicRelated: Fuzzy logic generalizes familiar Boolean operations to graded values.

• Distributive propertyRelated: Its two distributive laws show that distribution is not limited to ordinary arithmetic.

• George BooleBroader topic: It became the mathematical form most closely associated with Boole’s logic.

• Logical equivalenceNarrower topic: Its identities express propositional equivalences as algebraic rewrite laws.

• Binary operationRelated: Logical conjunction and disjunction are binary operations on truth values.

• Lattice (order theory)Broader topic: It adds distributivity and complements to the lattice structure.

• Digital logicNarrower topic: Its equations describe the logical behavior that digital circuits implement.

• William Stanley JevonsRelated: Jevons helped popularize and extend Boolean methods in nineteenth-century formal logic.

• Boolean functionNarrower topic: Its operations provide the standard language for expressing and manipulating Boolean functions.

• Bibliographic databaseRelated: Boolean operators combine or exclude terms in many database search interfaces.

• DisjunctionNarrower topic: Its operations provide an algebraic treatment of disjunction and its identities.

• CMOSRelated: CMOS transistor networks implement Boolean functions as logic gates.

• NAND gateNarrower topic: NAND’s behavior can be expressed as the negation of a conjunction.

• UltrafilterNarrower topic: Subsets form a Boolean algebra, where ultrafilters choose one of each element-complement pair.

• Complementary metal–oxide–semiconductorNarrower topic: CMOS gate networks implement Boolean functions as transistor arrangements.

• Digital circuitRelated: Boolean expressions describe the logic that gate networks implement.

• Forcing (mathematics)Related: Complete Boolean algebras provide an alternative presentation of forcing notions and truth values.

• OR gateNarrower topic: Its laws describe how OR gates combine and simplify within larger circuits.

• AND gateNarrower topic: Boolean algebra expresses the AND gate’s operation as multiplication-like conjunction.

• Digital computerRelated: Logic circuits implement Boolean operations on binary signals.

• Heyting algebraCompared with: Boolean algebras are precisely the Heyting algebras where every element equals its double negation.

• NOT gateNarrower topic: Boolean algebra expresses inversion as the complement operation, often written ¬A or A̅.

• Universal algebraBroader topic: Boolean algebras connect universal algebra to logic and digital circuit theory.

• Algebraic structureBroader topic: Boolean algebra connects algebraic laws to logic and digital circuit design.

• Augustus De MorganRelated: Its identities give an algebraic form to De Morgan’s laws.

• Boolean ringCompared with: It shares the Boolean name and has equivalent structure, but uses lattice operations rather than ring operations.

• Digital electronicsRelated: It provides the rules used to describe and simplify digital logic.

• History of logicRelated: It helped turn reasoning into symbolic calculation.

• XOR gateNarrower topic: Its identities describe how XOR combines with other logic operations.

• Hardware description languageNarrower topic: Combinational HDL expressions often implement Boolean functions.

• Karnaugh mapNarrower topic: Map groupings encode Boolean identities that eliminate variables from expressions.

• Arithmetic logic unitNarrower topic: Bitwise ALU operations implement Boolean functions independently across word bits.

• Electronic design automationNarrower topic: It supplies the logic that synthesis tools simplify and map into digital circuits.