Boolean Algebra (Logic)
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A Boolean Algebra (Logic) is a Mathematics that ...
- AKA: Boolean Algebra (Logic).
- See: Henry M. Sheffer, Statistics, Mathematics, Mathematical Logic, Abstract Algebra, Variable (Mathematics), Truth Value, Elementary Algebra, Logical Conjunction, Logical Disjunction, Negation, George Boole.
References
2017
- (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Boolean_algebra Retrieved:2017-8-14.
- 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 ¬. 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. [1] 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.
- 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 ¬. It is thus a formalism for describing logical relations in the same way that ordinary algebra describes numeric relations.
- ↑ "The name Boolean algebra (or Boolean 'algebras') for the calculus originated by Boole, extended by Schröder, and perfected by Whitehead seems to have been first suggested by Sheffer, in 1913." E. V. Huntington, "New sets of independent postulates for the algebra of logic, with special reference to Whitehead and Russell's Principia mathematica", in Trans. Amer. Math. Soc. 35 (1933), 274-304; footnote, page 278.