Boolean algebra

For other uses, see Boolean algebra (disambiguation).

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]

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  3. ^ Cite error: The named reference Huntington_1933 was invoked but never defined (see the help page).
  4. ^ Cite error: The named reference Peirce_1931 was invoked but never defined (see the help page).
  5. ^ Cite error: The named reference Givant-Halmos_2009 was invoked but never defined (see the help page).