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Boolean algebra - translation to Αγγλικά
Boolean algebra
![NOT]] gates.](https://commons.wikimedia.org/wiki/Special:FilePath/LogicGates.GIF?width=200 "NOT]] gates.")
VARIANT OF ORDINARY ELEMENTARY ALGEBRA
Laws of classical logic; Complement (Boolean algebra); Boolean Algebra; Boolean value; Boolean Logic; Boolean algebra (basic concepts); Boolean algebra (logic); Complete Boolean algebra (computer science); Logic function; Logic operation; Complement (boolean algebra); Boolean problem; Boolean equation; Boolean terms; Elementary Boolean algebra; Boolean logic; Boolean logic (computer science); Boolean logic in computer science; Introduction to Boolean algebra; Boolean searching; AND list; OR list; And List; Or List; And list; Or list; Boolean algebra (introduction); Introduction to boolean algebra; Boolean Connectors; Boolean attribute; Duality principle (Boolean algebra); Duality principle (boolean algebra); BooleanAlgebra; Switching algebra; Applications of boolean algebra; History of Boolean algebra; Logical algebra; Contact algebra; Boolean operator (Boolean algebra); Boolean operation (Boolean algebra); Boolean identity; Boolean identities; Boolian algebra; Boolian Algebra
Boolean algebra math. булева алгебра, алгебра логики
Boolean algebra
VARIANT OF ORDINARY ELEMENTARY ALGEBRA
Laws of classical logic; Complement (Boolean algebra); Boolean Algebra; Boolean value; Boolean Logic; Boolean algebra (basic concepts); Boolean algebra (logic); Complete Boolean algebra (computer science); Logic function; Logic operation; Complement (boolean algebra); Boolean problem; Boolean equation; Boolean terms; Elementary Boolean algebra; Boolean logic; Boolean logic (computer science); Boolean logic in computer science; Introduction to Boolean algebra; Boolean searching; AND list; OR list; And List; Or List; And list; Or list; Boolean algebra (introduction); Introduction to boolean algebra; Boolean Connectors; Boolean attribute; Duality principle (Boolean algebra); Duality principle (boolean algebra); BooleanAlgebra; Switching algebra; Applications of boolean algebra; History of Boolean algebra; Logical algebra; Contact algebra; Boolean operator (Boolean algebra); Boolean operation (Boolean algebra); Boolean identity; Boolean identities; Boolian algebra; Boolian Algebra
['bu:liən'ældʒibrə]
общая лексика
булева алгебра, алгебра логики
набор операций над двузначными логическими переменными, широко используемый в современных компьютерах. Названа в честь её создателя математика Джоржа Буля (George Boole, 1815-1864). Как правило, используются операции логического умножения, логического сложения и отрицания, так как из них можно построить любую другую булеву операцию. Все нынешние компьютеры построены на двузначной логике. Примером машин с трёхзначной логикой были ЭВМ "Сетунь" и "Сетунь-70" (Н.П. Брусенцов, МГУ)
вычислительная техника
булева алгебра
алгебра логики
Смотрите также
Boolean algebra
VARIANT OF ORDINARY ELEMENTARY ALGEBRA
Laws of classical logic; Complement (Boolean algebra); Boolean Algebra; Boolean value; Boolean Logic; Boolean algebra (basic concepts); Boolean algebra (logic); Complete Boolean algebra (computer science); Logic function; Logic operation; Complement (boolean algebra); Boolean problem; Boolean equation; Boolean terms; Elementary Boolean algebra; Boolean logic; Boolean logic (computer science); Boolean logic in computer science; Introduction to Boolean algebra; Boolean searching; AND list; OR list; And List; Or List; And list; Or list; Boolean algebra (introduction); Introduction to boolean algebra; Boolean Connectors; Boolean attribute; Duality principle (Boolean algebra); Duality principle (boolean algebra); BooleanAlgebra; Switching algebra; Applications of boolean algebra; History of Boolean algebra; Logical algebra; Contact algebra; Boolean operator (Boolean algebra); Boolean operation (Boolean algebra); Boolean identity; Boolean identities; Boolian algebra; Boolian Algebra
булева алгебра, алгебра логики
Ορισμός
Boolean algebra
<mathematics, logic> (After the logician George Boole)
1. Commonly, and especially in computer science and digital
electronics, this term is used to mean two-valued logic.
2. This is in stark contrast with the definition used by pure
mathematicians who in the 1960s introduced "Boolean-valued
models" into logic precisely because a "Boolean-valued
model" is an interpretation of a theory that allows more
than two possible truth values!
Strangely, a Boolean algebra (in the mathematical sense) is
not strictly an algebra, but is in fact a lattice. A
Boolean algebra is sometimes defined as a "complemented
distributive lattice".
Boole's work which inspired the mathematical definition
concerned algebras of sets, involving the operations of
intersection, union and complement on sets. Such algebras
obey the following identities where the operators ^, V, - and
constants 1 and 0 can be thought of either as set
intersection, union, complement, universal, empty; or as
two-valued logic AND, OR, NOT, TRUE, FALSE; or any other
conforming system.
a ^ b = b ^ a a V b = b V a (commutative laws)
(a ^ b) ^ c = a ^ (b ^ c)
(a V b) V c = a V (b V c) (associative laws)
a ^ (b V c) = (a ^ b) V (a ^ c)
a V (b ^ c) = (a V b) ^ (a V c) (distributive laws)
a ^ a = a a V a = a (idempotence laws)
--a = a
-(a ^ b) = (-a) V (-b)
-(a V b) = (-a) ^ (-b) (de Morgan's laws)
a ^ -a = 0 a V -a = 1
a ^ 1 = a a V 0 = a
a ^ 0 = 0 a V 1 = 1
-1 = 0 -0 = 1
There are several common alternative notations for the "-" or
logical complement operator.
If a and b are elements of a Boolean algebra, we define a <= b
to mean that a ^ b = a, or equivalently a V b = b. Thus, for
example, if ^, V and - denote set intersection, union and
complement then <= is the inclusive subset relation. The
relation <= is a partial ordering, though it is not
necessarily a linear ordering since some Boolean algebras
contain incomparable values.
Note that these laws only refer explicitly to the two
distinguished constants 1 and 0 (sometimes written as LaTeX
op and ot), and in two-valued logic there are no others,
but according to the more general mathematical definition, in
some systems variables a, b and c may take on other values as
well.
(1997-02-27)
Βικιπαίδεια
Boolean algebra
In mathematics and mathematical logic, Boolean algebra 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. Instead of elementary algebra, where the values of the variables are numbers and the prime operations are addition and multiplication, the main operations of Boolean algebra are the conjunction (and) denoted as ∧, the disjunction (or) denoted as ∨, and the negation (not) denoted as ¬.
