cơ sở dữ liệu_ phụ thuộc hàm và chuẩn hóa quan hệ - voer

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 1/20

CSDLIUSCIENCEANDTECHNOLOGY

PhthuchmvchunhaquanhTcgi:Ths.PhmHongNhung

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MtshngdnkhithitkcsdliuquanhVicquantrngnhtkhithitkcsdliuquanhltaphichnratpcclcquanhttnhtdatrnmtstiuchno.Vcclachntt,thchngtacncbitquantmnmirngbucgiaccdliutrongquanh,chnhlccphthuchm.

hiuhnvcuhitisaophithitkmtcsdliutt,chngtahycngtmhiuvdsau

RESULT(StNo,StName,SubNo,SubName,Credit,Mark)

QuanhRESULT(Ktquhctp)cccthuctnh:StNo(Msinhvin),StName(Tnsinhvin),SubNo(Mmnhc),SubName(Tnmnhc),Credit(Snvhctrnh)vMark(imthicasinhvintrongmnhc).

SauylminhhodliucaquanhRESULT

MinhhadliucaquanhRESULT

Quanhtrnthitkchattv

Dthadliu(Redundancy):Thngtinvsinhvinvmnhcblplinhiuln.NusinhvincmSt01thi10mnhcththngtinvsinhvinnyblpli10ln,tngtivimnhccmSub04,nuc1000sinhvinthiththngtinvmnhccnglpli1000lnKhngnhtqun(Inconsistency):Lhqucadthadliu.Gissabnghithnht,tnsinhvincchathnhNgathdliunylikhngnhtqunvibnghith2v3(vnctnlMai).Dthngkhithmb(Insertionanomalies):Numunthmthngtinmtsinhvinminhptrng(chacimmnhcno)voquanhthkhngcvkhochnhcaquanhtrngm2thuctnhStNovSubNo.Dthngkhixob(Deletionanomalies):Gisxoibnghicuicng,ththngtinvmnhccmmnhclSubNo=Sub07cngmt.

GIOTRNH

10Thch 10Chias

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 2/20

Nhnxt:Quaphntchtrn,tathychngtanntmcchtchquanhtrnthnhccquanhnhhn.

Trongchngnychngtasnghincuvnhngkhinimvccthuttoncththitkcnhnglcquanhtt.

Phthuchm(FunctionalDependencies)Phthuchm(FDs)csdnglmthconhgimtquanhtt.FDsvkhocsdngnhnghaccdngchuncaquanh.FDslnhngrngbucdliucsuyratnghavccmilinquangiaccthuctnh.

nhnghaphthuchmChor(U),virlquanhvUltpthuctnh.

ChoA,BU,phthuchmXY(clXxcnhY)cnhnghal:

t,trnut.X=t.Xtht.Y=t.Y

(Cnghal:NuhaibccngtrXthccngtrY)

Phthuchmcsuyratnhngquytcdliukhitakhostyucucabiton.

Tmsbohimxhi,tacthsuyractncanhnvin(SsnEname)Tmdn,tacthsuyratnvvtrcadn(PNumber{PName,PLcation})

BiudinFDsca2lcquanhEMP_DEPTvEMP_PROJ

HtinArmstrongCholcquanhr(U),Ultpthuctnh,Fltpccphthuchmcnhnghatrnquanhr.

TacphthuchmABcsuydinlogictFnuquanhrtrnUthaccphthuchmtrongFthcngthaphthuchmAB.

Tpphthuchm:F={AB,BC}

TacphthuchmAClphthuchmcsuytF.

HtinArmstrongcsdngtmraccphthuchmsuydintF.

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 3/20

HtinArmstrongbaogm:n

1.Phnx:NuYXthXY

2.Tngtrng:NuZUvXYthXZYZ(KhiuXZlXZ)

3.Bccu:NuXYvYZthXZ

4.Gibccu:NuXYvWYZthXWZ

5.Luthp:NuXYvXZthXYZ

6.Lutphnr:NuXYvZYthXZ

Trongsuluttrntha4,a5,a6suycta1,a2,a3.

BaongcatpphthuchmTagiflmtphthuchmcsuydntF,khiulFfnutntimtchuiphthuchm:f1,f2,.,fnsaochofn=fvmifilmtthnhvincaFhaycsuydntnhngphthuchmj=1,,i1trcnhvolutdn.BaongcaF:khiulF+ltpttcccphthuchmcsuytFnhvohtinArmstrong.F+cnhngha:

F+={XY|FXY}

BaongcatpthuctnhXtrnFBaongcatpthuctnhXxcnhtrntpphthuchmFkhiulX+ltphpttcccthuctnhcthsuyratX.Khiu:

X+={Y|FXY}

X+cthctnhtonthngquaviclpilplicquytc1,2,3cahtinArmstrong.

ThuttonxcnhbaongcatpthuctnhX+

X+:=X;repeatoldX+:=X+;for(miphthuchmYZtrongF)doifYX+thenX+Zuntil(oldX+=X+);

Chotpphthuchm

F={SSNENAME,PNUMBER{PNAME,PLOCATION},{SSN,PNUMBER}HOURS}Suyra:{SSN}+={SSN,ENAME}{PNUMBER}+={PNUMBER,PNAME,PLOCATION}{SSN,PNUMBER}+={SSN,PNUMBER,ENAME,PNAME,PLOCATION,HOURS}

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 4/20

Nhvy,tpthuctnh{SSN,PNUMBER}lkhocaquanh.

KhocaquanhChoquanhr(R),tpKRcgilkhacaquanhrnu:K+=RvnubtmtphntkhiKthbaongcanskhcR.

NhthtpKRlkhocaquanhnuK+=Rv(K\A)+R,AR.

ChoR={A,B,C,D,E,G}vtpphthuchm:

F={ABC,DEG,BEC,BCD,CGBD,ACDB,CEAG}

Tasthycctpthuctnh

K1={A,B},K2={B,E},K3={C,G},K4={C,E},K5={C,D},K6={B,C}ulkhacaquanh.

Nhvy,mtquanhcthcnhiukha.

Thuttontmkho

tng:BtuttpUvClosure(U+,F)=U.SautabtdnccphntcaUnhnctpbnhtmbaongcanvnbngU.

Thutton

Input:Lcquanhr(U),tpphthuchmF.Output:KhoKBc1:GnK=UBuc2:Lpliccbcsau:LoiphntAkhiKmClosure(KA,F)=U

Nhnxt

Thuttontrnchtmcmtkha.Nucntmnhiukha,tathayitrttloibccphntcaK.Chngtacthcithintcthchinthuttontrnbngcch:Trongbc1tachgnK=Left(ltpccphntcbntaytricaccphthuchm)

CholcquanhR={A,B,C,D,E,G,H,I}vtpphthuchm:

F={ACB,BIACD,ABCD,HI,ACEBCG,CGAE}

TmkhoK?

TacLeft={A,B,C,H,E,G}

Bc1:K=Left={A,B,C,H,E,G}

Bc2

Bc2

Tpthuctnh A B C D E G H I Ghich

ABCHEG x x x x x x x x

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 5/20

BCHEG x x x x x x x x LoiA

CHEG x x x x x x x x LoiB

CHG x x x x x x x x LoiE

Nhvy,{C,H,G}lmtkhocaR.

NumuntmttccckhocaR,tacnthayitrttloibphntcakhoK.

TpphthuchmtngngHaitpphthuchmFvGltngngnu

TtcccphthuchmtrongFcthcsuyratG,vTtcccphthuchmtrongGcthsuyratF.

Vth,FvGltngngnuF+=G+

NuFvGltngngthtaniFphGhayGphF.

Vth,thuttonsauyskimtrastngngcahaitpphthuchm:

FphE:XYE,tnhX+tF,saukimtraxemYX+EphF:XYF,tnhX+tE,saukimtraxemYX+

TpphthuchmtithiuTpphthuchmltithiununthomncciukinsau:

ChcmtthuctnhnmphabntaytricattcccphthuchmtrongF.KhngthbibtkmtphthuchmnotrongFmvnccmttpphthuchmtngngviF(tcl,khngcphthuchmdtha).KhngththaythbtkphthuchmXAnotrongFbngphthuchmYA,viYXmvnccmttpphthuchmtngngviF(tcl,khngcthuctnhdthatrongphthuchm)

Nhnxt:

Ttccctpphthuchmucphthuchmtithiutngngvin.Cthcnhiuphthuchmtithiu

Thutton:TmtpphthuchmtithiuGcaF

1.tG:F.2.ThaythttcccphthuchmX{A1,A2,,An}trongGbngnphthuchm:XA1,XA2,,XAn.3.VimiphthuchmXAtrongG,vimithuctnhBtrongXnu((G{XA}){(X{B})A})ltngngviG,ththaythXAbng(X{B})AtrongG.(Loibthuctnhdthatrongphthuchm)4.VimiphthuchmXAtrongG,nu(G{XA})tngngviG,thloibphthuchmXArakhiG.(Loibphthuchmdtha)

Ccdngchuncaquanh

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 6/20

nhnghaccdngchun

Dngchun1(FirstNormalForm)

nhngha

Mtquanhdngchun1nuccgitrcattcthuctnhtrongquanhlnguynt(tclchc1gitrtimtthiim).

Vd

Quanhsauykhngphidngchun1

DliucaquanhDEPARTMENTviphm1NFChuynquanhtrnthnhdngchun1(bngcchxcnhtpthuctnh{DNumber,DLocation}lkhochnh),tac:

Nhnxt

Quanhdngchun1ctntisdthadliu,trongquanhDEPARTMENT,nunhmtphngcnhiuaimkhcnhauthdliuca3thuctnh(DName,DNumber,DMgrSsn)blplinhiuln.ChngtacthtchquanhDEPARTMENTthnh2quanh:

QuanhDEPARTMENTctchthnh2quanh

Mtdliuca2quanhny

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 7/20

MinhhadliucaDEPARTMENTvDEPT_LOCATIONS

Dngchun2(SecondNormalForm_2NF)

nhngha

Mtquanhdngchun2nu

Quanhdngchun1Ttcccthuctnhkhngphilkhaphthucyvokha.Phthucy:PhthuchmYZlphthuchmynu:AY,(Y{A})Z

Smt

SmtNF2

Vd

QuanhEMP_PROJkhngphidngchun2vtnti2phthuchmFD2,FD3lphthuchmbphn(triviphthuchmy)

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 8/20

QuanhEmp_proj

Quanhsauydngchun2

QuanhEMP_DEPTdngchun2

MinhhodliucaquanhEMP_DEPT

Quanhsauydng2NF

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 9/20

MinhhodliucaquanhTHESIS

Nhnxt

Quanhdngchun2csdthathngtin.Dngchun2cthbviphmkhiquanhckhagmhnmtthuctnh.

Dngchun3(ThirdNormalForm)

nhngha

Mtquanhdngchun3nu

Quanhdngchun2Vkhngcchaccphthuchmphthucbccuvokho.Phthuchmphthucbccu:PhthuchmYZlphthuchmbccunutntihaiphthuchm:YXvXZ.

Biudinbngs

Dngchun3NF

Vd

QuanhEMP_DEPTkhngphidngchun3vcntntiphthuchmDNumberDName,DMgrSsnlphthuchmphthucbccuvokho.

QuanhEMP_DEPTkhngphidngchun3

Tchquanhtrnthnh2quanh:EMPLOYEEvDEPARTMENT.2quanhsauudngchun3

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 10/20

MtdliucaquanhEMPLOYEEvDEPARTMET

Nhnxt

Trongmtcsdliutt,ccquanhnncchuynvdngchun3.Tuynhin,dliuvnckhnngdthakhiquanhchaitpkhadtuyngilnnhau,hocquanhcthuctnhkhngkhaxcnhmtthuctnhkha.

DngchunBoyce_Codd(BoyceCoddNormalForm)

nhngha

QuanhRdngchunBCNFkhittcccphthuchmXAtrongRuphicXlkhocaR.

Vd

Quanhsaudng3NFnhngkhngphiBCNF.

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 11/20

MinhhodliucaquanhTEACHviphmchunBoyceCodd

nhncquanhBCNF,tacthtchquanhtrn:

Cch1:R1(Student,Instructor)vR2(Student,Course)

Cch2:R1(Couse,Instructor}vR2(Course,Student)

Cch3:R1(Instructor,Course}vR2(Instructor,Student)

VictchquanhnhtrnslmmtiphthuchmFD1.

Phpphnrcclcquanh

nhngha

PhpphnrcclcquanhR={A1,A2,...,An}lvicthaythlcquanhRthnhcclccon{R1,...,Rk},trongRiRvR=R1R2Rk

ChoquanhRviccphthuchmnhsau

LcquanhR

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 12/20

Tacthphnrthnh3lcR1(MaSV,TenSV,Lop)vPhpphnrkhngmtmtthngtin

ChoRlmt lcquanh,phpr=(R1,R2, . . .,Rn)vD l tpccphthucdliu.PhpphnrkhngmtmtthngtinnukhithchinphptonktnitnhinccquanhthnhphnR1,R2,,Rntavnnhncktqucaquanhbanu.

Vdvmtphpphnrcmtmtthngtin:

Choquanh

Quanhmu

MaSV MaMH iem

1 A 3

2 A 5

3 A 6

4 B 6

5 C 9

Nutaphnrquanhtrnthnh2quanh:R1(MaSV,MaMH)vR2(MaMH,iem)nhsau:

R1R2:

R1

MaSV MaMH

1 A

2 A

3 A

4 B

5 C

R2

MaMH iem

A 3

A 5

A 6

B 6

C 9

Thchinphpktnitnhin2quanhR1vR2:

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 13/20

R1*R2=

R1*R2

MaSV MaMH iem

1 A 3

1 A 5

1 A 6

2 A 3

2 A 5

2 A 6

3 A 3

3 A 5

3 A 6

4 B 6

5 C 9

Nhvy,khinitnhin2bng,tanhncquanhkhnggingquanhbanuPhpphnrtrnlmtmtthngtin.

Vntraivingithitklphitmranhngphpphnrkhnglmmtmtthngtin(chititsctrnhbyphnsau).Bygichngtastmhiumtthuttonkimtramtphpphnrcmtmtthngtinhaykhng.

Thuttonkimtraphpphnrkhngmtmtthngtin

Input

LcquanhR={A1,A2,...,An}TpccphthuchmFPhptch(R1,R2,...,Rk)

OutputKtlunphptchkhngmtmtthngtin.

Ccbccathutton

Bc1

Thitlpmtbngvinct(tngngvinthuctnh)vkdng(tngngvikquanh),trongctthjngvithuctnhAj,dngthingvilcRi.Tidngivctj,tainkhiuajnuthuctinhAjRi.Ngclitainkhiubij.

Bc2

XtccphthuchmtrongFvpdngchobngtrn.GistacphthuchmXYF,xtccdngcgitrbngnhautrnthuctnhXthlmbngccgitrcachngtrnY.Ngclilmbngchngbngkhiubij.Tiptcpdngccpthchobng(kcviclpliccphthuc

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 14/20

hmpdng)chotikhikhngcnpdngcna.

Bc3

Xemxtbngktqu.Nuxuthinmtdngchatongitra1,a2,,anthktlunphptchkhngmtmtthngtin.

Choquanh

MinhhadliucaquanhEMP_DEPT

Tchquanhtrnthnh2quanh

QuanhEMPLOYEEcphnr(tch)thnh2quanh

TpphthuchmF

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 15/20

TpphthuchmF

Kimtraphptchtrnlkhngmtmtthngtin:

Bc1

Bc1

EName SSN BDate Address DNumber DName DMgrSsn

EMPLOYEE a1 a2 a3 a4 a5 b16 b17

DEPARTMENT b21 b22 b23 b24 a5 a6 a7

Bc2:XtphthuchmDNumberDName,DMgrSsn.Tanhnthycgitra5dngth2,nntaslmbnggitra6,a7chodngth1.

Bc3:Tntimtdngchagitra1,a2,..a7.Ktlun,phpphnrtrnkhngmtmtthngtin.

Bc3

EName SSN BDate Address DNumber DName DMgrSsn

EMPLOYEE a1 a2 a3 a4 a5 a6 a7

DEPARTMENT b21 b22 b23 b24 a5 a6 a7

Sinhvinthchinphpnitnhin2quanhEMPLOYEEvDEPARTMENTtrnkimtracbngquanhbanuEMP_DEPT

ChunhoquanhChunhoquanhlvicphnrmtlcquanhthnhcclccondngchun3hocBCNFsaochovnbotonphthucvkhngmtmtdliu.

ThuttonphnrlcquanhthnhcclcquanhconBCNFInput

LcquanhRTpphthuchmF

Output

PhpphnrcaRkhngmtthngtinvmilcquanhtrongphptchudngBCNFiviphpchiucaFtrnlc.

Ccbccathutton

BanuphptchchbaogmR.NuSlmtlcthucvSchadngBCNFthchnphthuchmXAthatrongS,trongXkhngchakhacaSvAX.{phthuchmviphmnhnghadngchunBCNF}.ThaythStrongbiS1vS2nhsauS1=XA,S2=S\A.

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 16/20

QutrnhtrntiptcchonkhittccclcquanhudngBCNF

Vd

CholcquanhR(CTHRSG).

Trong:

C:CourseT:TeacherH:HourR:RoomS:StudentG:Group).VtpccphthuchmFCT:Mikhohc(course)cmtthy(teacher)duynht.HRC:Timtthiim(Hour)tiphnghc(room)chcmtkhohcduynht.HTR:TimtthiimvmtgiovinchmtphngduynhtCSG:Mtsinhvinhcmtcoursethchmtlpduynht.HSR:Mtsinhvin,mtthiimnhtnhchtrongmtphngduynht.

DavothuttontmkhoKhacaRlHS.

Yucu:TchlcRthnhcclccondngBCNF.

BiudinqutrnhtchquanhRthnhccquanhBCNF

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 17/20

Nhvy,quanhRctchthnh4quanhR1,R21,R221,R222uBCNF.

Thuttonphnrmtlcquanhthnhcclccon3NF.Input

LcquanhRTpccphthuchmF,khnglmmttnhtngqutgislphtithiu.

Output

PhptchkhngmtmtthngtintrnRthnhcclccondngchun3saochovnbotonccphthuchm.

Ccbccathutton

Bc1:LoibccthuctnhcaRnuthuctnhkhnglinquannphthuchmnocaF.(khngcmtchaivcaphthuchm).Bc2:NucmtphthuchmcaFlinquannttcccthuctnhcaRthktquchnhlR.Bc3:Ngoira,phptcharacclcgmccthuctnhXAngviphthuchmXAF.NutnticcphthuchmXA1,XA2,,XAnthucFththaythXAi(1

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 18/20

}

Yucu:

Tm{A}+={D,E,I,J}

TmkhacaquanhR.

TchquanhRthnhBCNF.

Kimtraxemvictchtrncmtmtthngtinkhng?

Lpliyucubi1vitpphthuchmsau

G={A,BC

B,DE,F

A,DG,H

AI

HJ}

Chomt quan h R ={CourseNo, SecNo, OfferingDept, Credit_Hours, CourseLevel, InstructorSSN, Semester,Year,Days_Hours,RoomNo,NoOfStudents}vtpphthuchm:

F={CourseNoOfferingDept,Credit_Hours,CourseLevel

CourseNo,SecNo,Semester,YearDays_Hours,RoomNo,NoOfStudents,InstructorSSN

RoomNo,Days_Hours,Semester,YearInstructorSSN,CourseNo,SecNo}

Yucu

TmkhacaquanhR.Quanhtrnthucdngchunmy?Tchquanhvdng3NF.Kimtraxemvictchtrncmtmtthngtinkhng?

Tweet 0 0 010Thch 10Chias

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 19/20

PluginxhicaFacebook

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Ths.PhmHongNhung(/profile/173)3GIOTRNH(/PROFILE/173?TYPES=2)|32TILIU(/PROFILE/173?TYPES=1)

NHGI:

NIDUNGCNGTCGI

MCLC

CsdliuCckhinimcbn(/c/cackhainiemcoban/d11e79e2/550371a9)Nhngkhinimvkintrccahthngcsdliu(/c/nhungkhainiemvakientruccuahethongcosodulieu/d11e79e2/a90615a2)Mhnhquanhthcth(EntityRelationshipModel)(/c/mohinhquanhethuctheentityrelationshipmodel/d11e79e2/ff2250a9)Mhnhcsdliuquanh(/c/mohinhcosodulieuquanhe/d11e79e2/cb8b15da)ChuyntmhnhERsangmhnhquanh(/c/chuyentumohinhersangmohinhquanhe/d11e79e2/3a0b6c88)Phthuchmvchunhaquanh(/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52)Thitkcsdliuvtl(/c/thietkecosodulieuvatly/d11e79e2/15b5b99d)

0datrn0nhgi

28/5/2015 Csdliu:PhthuchmvchunhaquanhVOER

https://voer.edu.vn/c/phuthuochamvachuanhoaquanhe/d11e79e2/91964a52 20/20

Kintrcnhnbn(Replication)(/m/kientrucnhanbanreplication/1fc54cf0)

Phthuchmvchunhaquanh(/m/phuthuochamvachuanhoaquanhe/91964a52)

Tngquanvnhgitruyvn(/m/tongquanvedanhgiatruyvan/1cde9f70)

Mhnhquanhthcth(EntityRelationshipModel)(/m/mohinhquanhethuctheentityrelationship

model/ff2250a9)

Tngquanvcchthngcsdliu(/m/tongquanvecachethongcosodulieu/583a66bf)

Ngnngiukhin(DCL)(/m/ngonngudieukhiendcl/1e499767)

TriggerPhnthchnh(/m/triggerphanthuchanh/1f729a7d)

Truyvndliu(Select)(/m/truyvandulieuselect/668008ec)

Cclnhquntrdliu(/m/caclenhquantridulieu/140fa679)

Tngquanvqunlgiaodch(/m/tongquanvequanlygiaodich/f8eee705)

TRC

TIP

Tmphtithiucatpphthuchm(/m/timphutoithieucuatapphuthuocham/8cc2e09a)

Mtsngnhnthnggp(/m/motsongonhanthuonggap/75c7960a)

BITPCHNG4KTS(/m/baitapchuong4kts/4a78eeee)

Chngminhbngcchphnchiatrnghp(/m/chungminhbangcachphanchiatruonghop/8041ff44)

Chngminhvacuous&ampChngminhtrivial(/m/chungminhvacuousampchungminhtrivial/87124b7e)

Tmkhatithiucalcquanh(/m/timkhoatoithieucualuocdoquanhe/112d363a)

ismnh(/m/daisomenhde/2cab0bb0)

Ccngnnglptrnhthngminh(/m/cacngonngulaptrinhthongminh/b720d330)

Phpkotheovpheptngng(/m/phepkeotheovapheptuongduong/54406fd0)

Vnphmvsphnlpvnphm(/m/vanphamvasuphanlopvanpham/7d342746)

TRC

TIP

NIDUNGTNGT

(https://www.facebook.com/voer.edu.vn)

ThvinHcliuMVitNam(VOER)ctitrbiVietnamFoundation(http://www.vnfoundation.org)vvnhnhtrnnntngHanoiSpring(http://www.hanoispring.com).CctiliuutunthgiyphpCreativeCommonsAttribution3.0trkhighichrngoil.