MA 301 Exam 1
Questions and Answers
Updated 2026
ABsetBconsistsBofBelementsB-BAnswerBaeS
TwoBsetsBareBequalBiffB-BAnswerBtheyBhaveBtheBsameBelements
ExactlyBoneBsetBwithBnoBelementsB-BAnswerBemptyBset,B∅
setBofBallBprimesB-BAnswerBT
ABsetBwithBoneBelementB-BAnswerB{∅}
DoesB∅B=B{∅}?B-BAnswerBNo
A⊆BBmeans?B-BAnswerBForBallBaBinBA,BthereBexistsBanBaBinBB
SubsetBsymbolB-BAnswerB⊆
properBsubsetBsymbolB-BAnswerB⊂
WhatBdoesBAB⊂BBBmeanB-BAnswerBAB⊆BB,BbutBABcannotBequalBB
SB⊆BABisBcalledBclosedBunderB*BifB-BAnswerBForBa,BbBinBS,Ba*bBisBinBS
, WeBsayBthatBaBbinaryBoperationB*BonBABisBcommutativeBifB-
BAnswerBforBallBa,BbBinBA:BaBtimesBbB=BbBtimesBa
AssociativeBifBforBallBa,Bb,BcBinBAB-BAnswerB(a*b)*c=a*(b*c)
WhatBisBaBnon-emptyBsetBSBwithBanBassociativeBbinaryBoperationBcalled?B-
BAnswerBABsemiBgroup
WhatBisBaBsemigroupBwithBanBidentityBelementBcalled?B-BAnswerBABmonoid
AnBelementBeBinBSBisBcalledBanBidentityBorBneutralBelementBifB-
BAnswerBforBallBxBinBS:BeB*BxB=BxB=BxB*Be
WhatBmakesBx'BanBinverseBofBx?B-BAnswerBxB*Bx'B=Bx'B*BxB=Be
HowBisBanBelementBunique?B-BAnswerBItBhasBanBidentityBelement
HowBcanBanBinverseBbeBunique?B-
BAnswerBTheBoriginalBisBuniqueBandBitBhasBanBinverse
HowBisBaBtableBcommunicative?B-BAnswerBItBisBsymmetricBacrossBtheBdiagonal
WhatBmakesBsomethingBanBequivalenceBrelation?B-BAnswerB1)Breflexive
2)Bsymmetric
3)Btransitive
WhatBareBtheBthreeBthingsBneededBtoBmakeBaBgroup?B-BAnswerB1)BAssociative
2)Bidentity
3)Binverse
Questions and Answers
Updated 2026
ABsetBconsistsBofBelementsB-BAnswerBaeS
TwoBsetsBareBequalBiffB-BAnswerBtheyBhaveBtheBsameBelements
ExactlyBoneBsetBwithBnoBelementsB-BAnswerBemptyBset,B∅
setBofBallBprimesB-BAnswerBT
ABsetBwithBoneBelementB-BAnswerB{∅}
DoesB∅B=B{∅}?B-BAnswerBNo
A⊆BBmeans?B-BAnswerBForBallBaBinBA,BthereBexistsBanBaBinBB
SubsetBsymbolB-BAnswerB⊆
properBsubsetBsymbolB-BAnswerB⊂
WhatBdoesBAB⊂BBBmeanB-BAnswerBAB⊆BB,BbutBABcannotBequalBB
SB⊆BABisBcalledBclosedBunderB*BifB-BAnswerBForBa,BbBinBS,Ba*bBisBinBS
, WeBsayBthatBaBbinaryBoperationB*BonBABisBcommutativeBifB-
BAnswerBforBallBa,BbBinBA:BaBtimesBbB=BbBtimesBa
AssociativeBifBforBallBa,Bb,BcBinBAB-BAnswerB(a*b)*c=a*(b*c)
WhatBisBaBnon-emptyBsetBSBwithBanBassociativeBbinaryBoperationBcalled?B-
BAnswerBABsemiBgroup
WhatBisBaBsemigroupBwithBanBidentityBelementBcalled?B-BAnswerBABmonoid
AnBelementBeBinBSBisBcalledBanBidentityBorBneutralBelementBifB-
BAnswerBforBallBxBinBS:BeB*BxB=BxB=BxB*Be
WhatBmakesBx'BanBinverseBofBx?B-BAnswerBxB*Bx'B=Bx'B*BxB=Be
HowBisBanBelementBunique?B-BAnswerBItBhasBanBidentityBelement
HowBcanBanBinverseBbeBunique?B-
BAnswerBTheBoriginalBisBuniqueBandBitBhasBanBinverse
HowBisBaBtableBcommunicative?B-BAnswerBItBisBsymmetricBacrossBtheBdiagonal
WhatBmakesBsomethingBanBequivalenceBrelation?B-BAnswerB1)Breflexive
2)Bsymmetric
3)Btransitive
WhatBareBtheBthreeBthingsBneededBtoBmakeBaBgroup?B-BAnswerB1)BAssociative
2)Bidentity
3)Binverse
