# 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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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.

D)Objective: (2.3)DescribeConditionsUnderWhichStatementIsTrue

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

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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

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• 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

C)D)

Objective: (2.3)DescribeSetinWords

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• 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

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• 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

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

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• 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

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23)

Explanation: Theexpression(AB)(AB)meansthesetofallelementsthatareintheunionbutnotintheintersection.

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)____________________

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