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1、Section2.1ñBasicSetOperations12ThisworkisprotectedbyUnitedStatescopyrightlawsandisprovidedsolelyfortheuseofinstructorsinteachingtheircoursesandassessingstudentlearning.Disseminationorsaleofanypartofthiswork(includingontheWorldWideWeb)willdestroytheint
2、egrityoftheworkandisnotpermitted.Theworkandmaterialsfromitshouldneverbemadeavailabletostudentsexceptbyinstructorsusingtheaccompanyingtextintheirclasses.Allrecipientsofthisworkareexpectedtoabidebytheserestrictionsandtohonortheintendedpedagogicalpurpose
3、sandtheneedsofotherinstructorswhorelyonthesematerials.AnalysiswithanIntroductiontoProof5thEditionbyStevenR.Layslay@leeuniversity.eduChapter2–SetsandFunctionsSolutionstoExercisesThefollowingnotationsareusedthroughoutthisdocument:8=thesetofnaturalnumber
4、s{1,2,3,4,…};=thesetofrationalnumbers<=thesetofrealnumbers"=“forevery”$=“thereexists”§=“suchthat”Section2.1–BasicSetOperations1.(a)True:Definition2.1.3.(b)False:8isthesetofpositiveintegers.(c)True:Example2.1.5.(d)True:Theorem2.1.7.Copyright©2014Pears
5、onEducation,Inc.Section2.1ñBasicSetOperations132.(a)False:A¶B=•meansAandBaredisjoint.(b)True:Definition2.1.8.(c)False:x≠ABmeansx≠AandxÆB.(d)False:ThisisOKtousesinceSbeingnonemptyistheonlynontrivialcase.3.Answerinbook:(a)True;(b)False;(c)True;(d)True;
6、(e)False;(f)False;(g)False;(h)True.4.(a){6,8};(b){2,4,6,8,10};(c){2,4};(d){6,8};(e){10};(f){5,7,10};(g)•;(h){5,7}.5.Theanswerto(a)isinthebook.Part(b)issimilar.6.(a)U;(b)•;(c)A¶B;(d)AßB;(e)A;(f)A.7.(a)Thediagramisthesameas(AßB)(A¶B);(b)•;(c)A;(d)UA.8
7、.(a)True.•isasubsetofeveryset.(b)True.•isanelementofS.(c)True.•isanelementofS,so{•}¨S.(d)True.{•}isanelementofS.9,10,and11areroutine.12.Beginningsentence:“Letx≠A”or“Supposex≠A”or“Ifx≠A…”Youwouldhavetoshowthatx≠B.13.Beginningsentence:“Letx≠A”or“Suppose
8、x≠A”or“Ifx≠A…”YouwouldhavetoshowthatxÆB.14.a,b,d.15.a,c.16.b,d.17.a,b,c,d.18.Thisisroutine.19.Hintinbook:SupposethatU=AßBandA¶B=•.ToshowA¨UB,letx≠A.ThenxÆB.(Why?)SincexisnotinB,whereisit?Ontheotherhand,toshowUB¨A,supposex≠UB.Expandwhatitmea
