Boolean logic: Difference between revisions

Revision as of 10:02, 7 February 2011

Revision as of 16:50, 17 February 2011

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'''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 Boole]], 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]].

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==Set logic vs. Boolean logic==

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Sets can contain any elements. We will first start out by discussing general set logic, then restrict ourselves to Boolean logic, where elements (or "bits") each contain only two possible values, called various names, such as "true" and "false", "yes" and "no", "on" and "off", or "1" and "0".

==Terms==

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[[Image:Venn A intersect B.svg|thumb|300px|right|Venn diagram showing the intersection of sets "A AND B" (in violet/dark shading), the union of sets "A OR B" (all the colored regions), and the exclusive OR case "set A XOR B" (all the colored regions except the violet). The "universe" is represented by all the area within the rectangular frame.]]