每周一交作业,作业成绩占总成绩的10%；平时不定期的进.ppt

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1、每周一交作业，作业成绩占总成绩的10%；平时不定期的进行小测验，占总成绩的20%；期中考试成绩占总成绩的20%；期终考试成绩占总成绩的50%A∪B=A∪C⇏B=Ccancellationlaw。Example:A={1,2,3},B={3,4,5},C={4,5},BC,ButA∪B=A∪C={1,2,3,4,5}Example:A={1,2,3},B={3,4,5},C={3},BC,ButA∩B=A∩C={3}A-B=A-C⇏B=Ccancellationlaw:symmetricdiffe

2、renceThesymmetricdifferenceofAandB,writeAB,isthesetofallelementsthatareinAorB,butarenotinbothAandB,i.e.AB=(A∪B)-(A∩B)。(A∪B)-(A∩B)=(A-B)∪(B-A)Theorem1.4:ifAB=AC,thenB=CDistributivelawsandDeMorgan’slaws:B∩(A1∪A2∪…∪An)=(B∩A1)∪(B∩A2)∪…∪(B∩An)B∪(A1∩A2∩…∩

3、An)=(B∪A1)∩(B∪A2)∩…∩(B∪An)Chapter2RelationsDefinition2.1:Anorderpair(a,b)isalistingoftheobjectsaandbinaprescribedorder,withaappearingfirstandbappearingsecond.Twoorderpairs(a,b)and(c,d)areequalifonlyifa=candb=d.{a,b}={b,a}，orderpairs:(a,b)(b,a)unlessa=b

4、.(a,a)Definition2.2:Theorderedn-tuple(a1,a2,…,an)istheorderedcollectionthathasa1asitsfirstelement,a2asitssecondelement,…,andanasitsnthelement.Twoorderedn-tuplesareequalisonlyifeachcorrespondingpairoftheirelementsiaequal,i.e.(a1,a2,…,an)=(b1,b2,…,bn)ifon

5、lyifai=bi,fori=1,2,…,n.Definition2.3:LetAandBbetwosets.TheCartesianproductofAandB,denotedbyA×B,isthesetofallorderedpairs(a,b)whereaAandbB.HenceA×B={(a,b)

6、aAandbB}Example:LetA={1,2},B={x,y},C={a,b,c}.A×B={(1,x),(1,y),(2,x),(2,y)};B×A={(x,1),(x,2),(y,

7、1),(y,2)};B×AA×Bcommutativelaws×A×C={(1,a),(1,b),(1,c),(2,a),(2,b),(2,c)};A×A={(1,1),(1,2),(2,1),(2,2)}。A×=×A=Definition2.4:LetA1,A2,…Anbesets.TheCartesianproductofA1,A2,…An,denotedbyA1×A2×…×An,isthesetofallorderedn-tuples(a1,a2,…,an)whereaiAifori=

8、1,2,…n.HenceA1×A2×…×An={(a1,a2,…,an)

9、aiAi,i=1,2,…,n}.Example:A×B×C={(1,x,a),(1,x,b),(1,x,c),(1,y,a),(1,y,b),(1,y,c),(2,x,a),(2,x,b),(2,x,c),(2,y,a),(2,y,b),(2,y,c)}。IfAi=Afori=1,2,…,n,thenA1×A2×…×AnbyAn.Example：LetArepresentthesetofallstudentsatanunive

10、rsity,andletBrepresentthesetofallcourseattheuniversity.WhatistheCartesianproductofA×B?TheCartesianproductofA×Bconsistsofalltheorderedpairsoftheform(a,b),whereaisastudentattheuniversityandbisacourseofferedattheuniversity.ThesetA×B