Difference between revisions of "Boolean algebra"
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| − | In [[mathematics]] and [[mathematical logic]], '''Boolean algebra''' is the branch of [[algebra]] in which the values of the variables are the [[Truth value|truth values]] true and false, usually denoted 1 and 0 respectively. | + | In [[mathematics]] and [[mathematical logic]], '''Boolean algebra''' (or '''Boolean logic''') is the branch of [[algebra]] in which the values of the variables are the [[Truth value|truth values]] true and false, usually denoted 1 and 0 respectively. |
== Description == | == Description == | ||
| − | + | The main operations of Boolean algebra are the conjunction and, denoted ∧, the disjunction or, denoted ∨, and the negation not, denoted ¬. | |
| + | |||
| + | It is thus a formalism for describing logical relations in the same way that ordinary algebra describes numeric relations. | ||
By contrast, in [[elementary algebra]] the values of the variables are [[Number|numbers]], and the main operations are [[addition]] and [[multiplication]]. | By contrast, in [[elementary algebra]] the values of the variables are [[Number|numbers]], and the main operations are [[addition]] and [[multiplication]]. | ||
| Line 22: | Line 24: | ||
* [[Algebra]] | * [[Algebra]] | ||
| + | * [[Binary number]] | ||
* [[George Boole]] | * [[George Boole]] | ||
| + | * [[Boole's syllogistic]] is a logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the "empty set." | ||
| + | * [[Boolean algebra (structure)]], a set with operations resembling logical ones | ||
| + | * [[Boolean algebras canonically defined]] | ||
| + | * [[Boolean circuit]], a [[mathematical model]] for digital logical circuits. | ||
| + | * [[Boolean data type]] is a [[data type]], having two values (usually denoted true and false) | ||
| + | * [[Boolean expression]], an expression in a programming language that produces a Boolean value when evaluated | ||
| + | * [[Boolean function]], a function that determines Boolean values or operators | ||
| + | * [[Boolean model (probability theory)]], a model in stochastic geometry | ||
| + | * [[Boolean network]], a certain network consisting of a set of Boolean variables whose state is determined by other variables in the network | ||
| + | * [[Boolean processor]], a 1-bit variables computing unit | ||
| + | * [[Boolean satisfiability problem]] | ||
| + | * [[Booleo]] | ||
| + | * [[Heyting algebra]] | ||
| + | * [[Intuitionistic logic]] | ||
| + | * [[List of Boolean algebra topics]] | ||
* [[Logic]] | * [[Logic]] | ||
| + | * [[Logic design]] | ||
* [[Mathematics]] | * [[Mathematics]] | ||
* [[Mathematical logic]] | * [[Mathematical logic]] | ||
* [[Operation (mathematics)]] | * [[Operation (mathematics)]] | ||
| + | * [[Propositional calculus]] | ||
| + | * [[Relation algebra]] | ||
| + | * [[Vector logic]] | ||
== External links == | == External links == | ||
Latest revision as of 06:03, 29 May 2016
In mathematics and mathematical logic, Boolean algebra (or Boolean logic) is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.
Description
The main operations of Boolean algebra are the conjunction and, denoted ∧, the disjunction or, denoted ∨, and the negation not, denoted ¬.
It is thus a formalism for describing logical relations in the same way that ordinary algebra describes numeric relations.
By contrast, in elementary algebra the values of the variables are numbers, and the main operations are addition and multiplication.
History
Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847), and set forth more fully in his An Investigation of the Laws of Thought (1854).
According to Huntington, the term "Boolean algebra" was first suggested by Sheffer in 1913.
Applications
Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages.
It is also used in set theory and statistics.
See also
- Algebra
- Binary number
- George Boole
- Boole's syllogistic is a logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the "empty set."
- Boolean algebra (structure), a set with operations resembling logical ones
- Boolean algebras canonically defined
- Boolean circuit, a mathematical model for digital logical circuits.
- Boolean data type is a data type, having two values (usually denoted true and false)
- Boolean expression, an expression in a programming language that produces a Boolean value when evaluated
- Boolean function, a function that determines Boolean values or operators
- Boolean model (probability theory), a model in stochastic geometry
- Boolean network, a certain network consisting of a set of Boolean variables whose state is determined by other variables in the network
- Boolean processor, a 1-bit variables computing unit
- Boolean satisfiability problem
- Booleo
- Heyting algebra
- Intuitionistic logic
- List of Boolean algebra topics
- Logic
- Logic design
- Mathematics
- Mathematical logic
- Operation (mathematics)
- Propositional calculus
- Relation algebra
- Vector logic
External links
- Boolean algebra @ Wikipedia
