300 2) Name MULTIPLE CHOICE. placed the - American ... 300 Exam 1 Review (Ch. 2) Name_____ _____ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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  • Math300Exam1Review(Ch.2) Name_________________________________________________________________________________________________________________________________________MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

    Decidewhether,,both,orneithercanbeplacedintheblanktomakeatruestatement.1) {0}

    A) Bothand B) C) Neither D) 1)

    Explanation: A)B)C) RememberthatABmeansthateveryelementofAisalsoinB.So{0}Bisnot

    true,since0isin{0},butnotin.RememberalsothatABmeansthateveryelementofAisalsoinB,andthatBhasatleastoneelementthatisnotinA.Buthasnoelementsinit,sothisclearlydoesnotapply.

    D)Objective: (2.2)IdentifyProperSubsets

    Describetheconditionsunderwhichthestatementistrue.2) AB=B

    A) Alwaystrue B) BA C) A B D) A=2)

    Explanation: A)B)C) RememberthatABmeansthesetcontainingallelementsfrombothsetsAandB.

    Inotherwords,itistheresultofcombiningsetsAandB.IfthecombinationofsetsAandBisthesameassetB,thenallelementsofAmustalreadybeinB.ThusAB.

    D)Objective: (2.3)DescribeConditionsUnderWhichStatementIsTrue

    3) AA=AA) Alwaystrue B) A C) A= U D) A=

    3)

    Explanation: A)B)C)D) RememberthatAisthecomplementofA,meaningthesetcontainingeverything

    intheuniversalsetoutsideofA.ThusAandAhavenoelementsincommon,sotheirintersectionisempty.SoweknowthatAA=.Therefore,theonlywaythatAAcanbeequaltoAisifA=.

    Objective: (2.3)DescribeConditionsUnderWhichStatementIsTrue

    Determinewhetherthestatementistrueorfalse.Let A={1,3,5,7}

    B={5,6,7,8}C={5,8}D={2,5,8}U={1,2,3,4,5,6,7,8}

    4) DBA) True B) False

    4)

    Explanation: A) Dcontainstheelement2,whichisnotinB.ThusDisnotasubsetofB.B)

    Objective: (2.2)DetermineTruthofStatement:Subsets

    1

  • 5) AA) True B) False

    5)

    Explanation: A) RememberthatABmeansthateveryelementofAisalsoanelementofB.ThisisequivalenttosayingthatAcontainsnoelementsthatarenotinB.Therefore,theemptysetmustbeasubsetofeveryset.(Notethatsinceisempty,itcontainsnoelementsthatarenotinBnomatterwhatBis.Infact,containsnoelementswhatsoever.

    B)Objective: (2.2)DetermineTruthofStatement:Subsets

    LetAandBbesetswithcardinalnumbers,n(A)= aandn(B)= b,respectively.Decidewhetherthestatementistrueorfalse.

    6) n(AB)=n(A)+n(B)-n(AB)A) True B) False

    6)

    Explanation: A) RememberthatABisthesetcontainingallelementsthatbelongtoAorB(orboth).Son(A)+n(B)hascountedanyelementsofABtwice,andthatswhyweneedtosubtractn(AB)tomakeupforcountingthemtwice.

    B)Objective: (2.3)DetermineTruthofStatement:CardinalNumbers

    7) n(AB)=n(A)-n(B)A) True B) False

    7)

    Explanation: A)B) Heresacounterexample:LetA= {1,2,3,4}andB= {1}.Thenn(AB)=1,butn(A)-n(B)=4-1=3.Thisprovesthatthestatmentisnottrueinallcases.

    Objective: (2.3)DetermineTruthofStatement:CardinalNumbers

    LetU={allsodapops},A={alldietsodapops},B= {allcolasodapops},C= {allsodapopsincans},andD={allcaffeine-freesodapops}.Describethesetinwords.

    8) ACA) AlldietsodapopsandallsodapopsincansB) Allnon-dietsodapopsincansC) AlldietsodapopsincansD) Allnon-dietsodapopsandallsodapopsincans

    8)

    Explanation: A)B) ACmeansthesetofallelementsthatareinCbutnotinA.Anelementbeingin

    Cmeansthatitisasodapopinacan.NotbeinginAmeansthatitisnotadietsodapop.Sotheintersectionofthesesetsisthesetofallnon-dietsodapopsincans.

    C)D)

    Objective: (2.3)DescribeSetinWords

    2

  • Listtheelementsintheset.Let U={q,r,s,t,u,v,w,x,y,z}

    A={q,s,u,w,y}B={q,s,y,z}C={v,w,x,y,z}.

    9) BCA) {w,y,z} B) {q,s,v,w,x,y,z}C) {y} D) {y,z}

    9)

    Explanation: A)B)C)D) BCmeansthesetofallelementscommontoBandC.Wecanseethatyandzare

    theonlyelementsthatBandChaveincommon.Objective: (2.3)UseSetOperationsI

    10) ABA) {u,w} B) {t,v,x}C) {r,s,t,u,v,w,x,z} D) {q,s,t,u,v,w,x,y}

    10)

    Explanation: A) ABmeansthesetofallelementsthatareinAbutnotinB.Wecanseethatuandwaretheonlyelementsthatfietthisdescription.

    B)C)D)

    Objective: (2.3)UseSetOperationsI

    11) B(A-C)A) {q,r,s,t,u,v,w,x,y} B) {q,s,u,y}C) {q,s,u,y,z} D) {q,s}

    11)

    Explanation: A)B)C)D) B(A-C)meansthesetofallelementsthatareinBandinAbutnotinC.Wecan

    seethatqandsaretheonlyelementsbelongingtothisset.Objective: (2.3)UseSetOperationsII

    Tellwhetherthestatementistrueorfalse.12) {8}={x|xisanevencountingnumberbetween10 and16}

    A) True B) False12)

    Explanation: A)B) Thesetofallcountingnumbersbetween10and16istheset{11,12,13,14,15}.

    Objective: (2.1)DetermineTruthofStatement:SetsI

    Useorintheblanktomakeatruestatement.13) {e,n,j}{e,e,n,n,j,j}

    A) B) 13)

    Explanation: A)B) Thesetwosetsareequal-- theybothcontaintheelementse,nandj(remember

    thatlistingelementsmorethanoncedoesntchangetheset).Therefore,theyarebothsubsetsofeachother,soBistherightchoice.

    Objective: (2.2)DetermineSubsetRelationships

    3

  • Writethesetinset-buildernotation.14) {17,18,19,20}

    A) {x|xisanintegerlessthan21} B) {x|xisanintegerbetween16and21}C) {17,18,19,20} D) {x|xisanintegerbetween17and20}

    14)

    Explanation: A) Thisis{1,2,3,...,20}B) Clearly,17,18,19and20aretheintegersbetween16and21.C) ThisisnotwritteninsetbuildernotationD) Thesetdescribedis{18,19}

    Objective: (2.1)UseSet-BuilderNotation

    SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

    DrawanappropriateVenndiagramandusethegiveninformationtofillinthenumberofelementsineachregion.15) n(A)=48,n(B)=60,n(C)=51,n(AB)= 20,n(B C)= 19,n(A C)= 18,

    n(ABC)=12,n(AB)=7015)

    Explanation:Objective: (2.4)DrawVennDiagram,LabelSizeofEachRegion

    Findtheindicatedcardinalnumber.16) Findn(G),giventhatn(DG)=20andD= {7,8,9,10}. 16)

    Explanation: Weknowthatn(DG)= n(D) n(G)= 4 n(G)= 20,son(G)mustbe5.

    Objective: (2.3)FindCardinalNumber:CartesianProducts

    Findn(A)fortheset.

    17) A= 12,-1

    2, 23,-2

    3, 34,-3

    4,..., 19

    20,-19

    2017)

    Explanation: n(A)meansthenumberofelementsinA.Weseethatthedenominatorsoccurinpairs,andthatthereare20-1=19pairs,whichcomesoutto38elements.

    Objective: (2.1)Findn(A)forSet

    FindtheCartesianproduct.18) A={2,4,7,6}

    B={0,1}FindBA.

    18)

    Explanation: RememberthedefinitionofCaresianproduct::A B= {(x,y)|xAandyB}

    Objective: (2.3)FindCartesianProduct

    4

  • Findthecardinalnumberoftheindicatedset.Usethecardinalnumberformula.19) Ifn(A)=7,n(B)=15andn(AB)=5,whatisn(A B)? 19)

    Explanation: n(AB)=n(A)+n(B)-n(AB)

    Objective: (2.4)UseFormulatoFindCardinalNumber

    Findthecardinalnumberoftheset.20) ThenumbersintheVennDiagrambelowrepresentcardinalities.

    Findn(ABC)

    20)

    Explanation: Theexpressionn(ABC)meansthenumberofelementsthatbelongtoAandC,butnotB.

    Objective: (2.4)DetermineCardinalityfromVennDiagram

    Findthenumberofsubsetsoftheset.21) {math,English,history,science,art} 21)

    Explanation: RememberthatthenumberofsubsetsofandsetAisequalto2n(A).

    Objective: (2.2)FindNumberofSubsets

    Forthegivensets,constructaVenndiagramandplacetheelementsintheproperregion.22) LetU={c,d,g,h,k,u,q}

    A={d,h,g,q}B={c,d,h,u}

    22)

    Explanation:

    Objective: (2.3)PlaceElementsinVennDiagram

    5

  • Shadetheregionsrepresentingtheset.23) (AB)(AB)

    23)

    Explanation: Theexpression(AB)(AB)meansthesetofallelementsthatareintheunionbutnotintheintersection.

    Objective: (2.3)ShadeVennDiagram

    Solvetheproblem.24) Listallpossiblesubsetsoftheset{m,n}. 24)

    Explanation: Rememberthatisasubsetofanyset.

    Objective: (2.2)ListSubsetsofSet

    ThelistsbelowshowfiveagriculturalcropsinAlabama,Arkansas,andLouisiana.

    Alabama Arkansas Louisianasoybeans(s) soybeans(s) soybeans(s)peanuts(p) rice(r) sugarcane(n)corn(c) cotton(t) rice(r)hay(h) hay(h) corn(c)wheat(w) wheat(w) cotton(t)

    LetUbethesmallestpossibleuniversalsetthatincludesallofthecropslisted,andletA,KandLbethesetsoffivecropsinAlabama,Arkansas,andLouisiana,respectively.Findeachofthefollowingsets.

    25) ThesetofcropsinA. 25)Explanation: ThesearetheonlycropsnotgrowninAlabama.

    Objective: (2.2)SolveApps:FindComplement/Intersection

    26) LetA={(x,y)|x2+y2=25}andB={(x,y)|y-x=1}.FindA B .Objective:

    26)____________________

    6

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