Crossword clues for boolean algebra
boolean algebra
Wikipedia
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized truth values. It is also a special case of a De Morgan algebra and a Kleene algebra (with involution).
Every Boolean algebra gives rise to a Boolean ring, and vice versa, with ring multiplication corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨). However, the theory of Boolean rings has an inherent asymmetry between the two operators, while the axioms and theorems of Boolean algebra express the symmetry of the theory described by the duality principle. __TOC__
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 main operations are addition and multiplication, 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.
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.
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.
Boolean algebra is the algebra of truth values and operations on them.
Boolean algebra may also refer to:
- Boolean algebra (structure), any member of a certain class of mathematical structures that can be described in terms of an ordering or in terms of operations on a set
- Boolean ring
Usage examples of "boolean algebra".
This was an animated introduction to sets, leading into Boolean Algebra, with color as an additional tool.
Amrita was retreating into a world of number theory and Boolean Algebra.
The actual content was zero, as honest metaphysics must be, but I loaded it with Boolean algebra, which (if solved) proved that Dzhugashvili was a murdering scoundrel.
It went through physics, astronomy, molecular biology, inorganic chemistry, differential calculus, and Boolean algebra like hydrochloric acid through gossamer.