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1、PARTⅡCOMPUTERSOFTWARECHAPTER3MATHEMATICFUNDAMENTALS3.1BOOLEANALGEBRAchapter3-3.13.1BOOLEANALGEBRA*MainpointMainpoint:●Developmentandfunctionofbooleanalgebra●Conceptofsetalgebra●Setoperations●Booleanoperations计算机英语（第三版）*?1计算机英语（第三版）TheconceptofaBooleanalgebraw
2、asfirstproposedbytheEnglishmathematicianGeorgeBoolein1847.Sincethattime,Boole’soriginalconceptionhasbeenextensivelydevelopedandrefinedbyalgebraistsandlogicians［1］.TherelationshipsamongBooleanalgebra,setalgebra,logic,andbinaryarithmetichavegivenBooleanalgebras
3、acentralroleinthedevelopmentofelectronicdigitalcomputers.?1●Whatisthefundamentalsofelectronicdigitalcomputers?计算机英语（第三版）Themostintuitivedevelopmentofbooleanalgebrasarisesfromtheconceptofasetalgebra.LetS={a,b,c}andT={a,b,c,d,e}betwosetsconsistingofthreeandfive
4、elements,respectively.WesaythatSisasubsetofT,sinceeveryelementofS(namely,a,b,andc)belongstoT.SinceThasfiveelements,thereare25subsetsofT,forwemaychooseanyindividualelementtobeincludedoromittedfromasubset［2］.Notethatthese32subsetsincludeTitselfandtheemptyset,wh
5、ichcontainsnoelementsatall［3］.原因状语从句原因状语从句计算机英语（第三版）IfTcontainsallelementsofconcern,itiscalledtheuniversalset.GivenasubsetofT,suchasS,wemaydefinethecomplementofSwithrespecttoauniversalsetTtoconsistofpreciselythoseelementsofTwhicharenotincludedinthegivensubset
6、［4］.Thus,Sasabovedefinedhasasitscomplement(withrespecttoT)S={d,e}.Theunionofanytwosets(subsetsofagivenset)consistsofthoseelementsthatareinoneortheotherorinbothgivensets［5］;theintersectionoftwosetsconsistsofthoseelementsthatareinbothgivensets.宾语补足语定语从句定语从句定语从句
7、Weusethesymbol∪todenotetheunion,and∩todenotetheintersectionoftwosets.Forexample,ifB={b,d,e},thenB∪S={a,b,c,d,e},andB∩S={b}.*?2计算机英语（第三版）?2●ExplaintheoperationsofunionandintersectionWhileothersetoperationsmaybedefined［6］,theoperationsofcomplementation,union,an
8、dintersectionareofprimaryinteresttous.让步状语从句ABooleanalgebraisafiniteorinfinitesetofelementstogetherwiththreeoperations—negation,addition,andmultiplication—thatcorrespondtothesetoperations
