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m GETTING RID OF ANNOYING "UNDUE SECTION" TAGS THAT ARE ON EVERY SINGLE SECTION AND PUTTING IT AT THE TOP OF THE PAGE, PEOPLE. REALLY, I CAN'T READ THIS ARTICLE. |
m GETTING RID OF ANNOYING "UNDUE SECTION" TAGS THAT ARE ON EVERY SINGLE SECTION AND PUTTING IT AT THE TOP OF THE PAGE, PEOPLE. REALLY, I CAN'T READ THIS ARTICLE. |
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{{Original research|date=August 2010}}
{{Merge to|Introduction to Boolean algebra|date=February 2010}}
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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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==Terms==
[[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.]]
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==Example==
Imagine that set A contains all even numbers (multiples of two) in "the universe" (defined in the example below as all integers between 0 and 30 inclusive) and set B contains all multiples of three in "the universe". Then the '''intersection''' of the two sets (all elements in sets A AND B) would be all multiples of six in "the universe". The complement of set A (all elements NOT in set A) would be all odd numbers in "the universe".
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===Database applications===
[[Relational databases]] use [[SQL]], or other database-specific languages, to perform queries, which may contain Boolean logic. For this application, each record in a table may be considered to be an "element" of a "set". For example, in SQL, these [[SELECT]] statements are used to retrieve data from tables in the database:
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