# Theorems of Boolean algebra

May 29th, 2015
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After values, the next ingredient of any algebraic system is its operations. Whereas elementary algebra is based on numeric operations multiplication xy, addition x + y, and negation −x, Boolean algebra is customarily based on logical

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Boolean algebra (logic)From Wikipedia, the free encyclopediaFor other uses, seeBoolean algebra (disambiguation).Boolean algebra(orBoolean logic) is a logical calculus oftruth values, developed byGeorge Boolein the 1840s. It resembles thealgebraofreal numbers, but with the numeric operations of multiplicationxy, additionx+y, and negation xreplaced by the respective logical operations ofconjunctionxy,disjunctionxy, andnegationx. The Boolean operations are these and all other operations that can be built from these, such asx(yz). These turn out to coincide with the set of all operations on the set {0,1} that take only finitely many arguments; there are 22nsuch operations when there arenarguments.The laws of Boolean algebra can be definedaxiomaticallyas certain equations called axioms together with theirlogical consequencescalled theorems, orsemanticallyas those equations that are true for every possible assignment of 0 or 1 to their variables. The axiomatic approach issoundandcompletein the sense that it proves respectively neither more nor fewer laws than the semantic approach.ValuesBoolean algebra is the algebra of two values. These are usually taken to be 0 and 1, as we shall do here, although F and T, false and true, etc. are also in common use. For the purpose of understanding Boolean algebra anyBoolean domainof two values will do.Regardless of nomenclature, the values are c

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