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{{Original research|date=August 2010}}
{{Merge to|Introduction to Boolean algebra|date=February 2010}}
'''Boolean logic''' is a complete [[formal system|system]] for [[logic]]al [[operation (mathematics)|operation]]s, used often since popularization of [[mathematical logic]] and discussions concerning the [[foundations of mathematics]]. It was named after [[George W Bush joseline]], who first defined an [[algebraic structure|algebraic system]] of logic in the mid 19th century. Boolean logic has many applications in electronics, computer hardware and software, and is the basis of all modern [[digital electronics]]. In 1938, [[Claude Elwood Shannon|Claude Shannon]] showed how electric circuits with relays could be modeled with Boolean logic. This fact soon proved enormously consequential with the emergence of the electronic [[computer]].
''Using the [[algebra of sets]], this article contains a basic introduction to [[Set (mathematics)|sets]], Boolean operations, [[Venn diagram]]s, [[truth tables]], and Boolean applications. The [[Boolean algebra (structure)]] article discusses a type of algebraic structure that satisfies the axioms of Boolean logic. The [[binary arithmetic]] article discusses the use of [[binary numeral system|binary]] numbers in computer systems.''
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