*World of Mathematics*. ©2005-2006 Thomson Gale, a part of the Thomson Corporation. All rights reserved.

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## Boolean Algebra

Boolean **algebra** is often referred to as the algebra of logic, because the English mathematician **George Boole**, who is largely responsible for its beginnings, was the first to apply algebraic techniques to logical methodology. Boole showed that logical **propositions** and their connectives could be expressed in the language of **set theory**. Thus, Boolean algebra is also the **algebra of sets**. Algebra, in general, is the language of mathematics, together with the rules for manipulating that language. Beginning with the members of a specific set (called the universal set), together with one or more binary operations defined on that set, procedures are derived for manipulating the members of the set using the defined operations, and combinations of those operations. Both the language and the rules of manipulation vary, depending on the properties of elements in the universal set. For instance, the algebra of **real numbers** differs from...

This section contains 910 words(approx. 4 pages at 300 words per page) |