# Boolean algebra

## Algebraic manipulation of "true" and "false" / From Wikipedia, the free encyclopedia

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In mathematics and mathematical logic, **Boolean algebra** is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values *true* and *false*, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (*and*) denoted as ∧, disjunction (*or*) denoted as ∨, and negation (*not*) denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations.

Boolean algebra was introduced by George Boole in his first book *The Mathematical Analysis of Logic* (1847),^{[1]} and set forth more fully in his *An Investigation of the Laws of Thought* (1854).^{[2]}
According to Huntington, the term "Boolean algebra" was first suggested by Henry M. Sheffer in 1913,^{[3]} although Charles Sanders Peirce gave the title "A Boolian [*sic*] Algebra with One Constant" to the first chapter of his "The Simplest Mathematics" in 1880.^{[4]} 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.^{[5]}