离散数学课后习题答案(左孝凌版)

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12a)᝞ᜩ4ᡃe஺`Pᜩ஺Qᡃe஺PfQ⌮ᣚCQ-P⊤{⚪:᝞ᡃe4ᑣᜩ஺⌮C⊤{⚪:᝞ᡃ4ᑣᜩeb)+,ᡃᶇ஺`S+,-஺Rᡃᶇ஺R-S⌮ᣚCS-R⊤{⚪᝞+,-ᑣᡃᶇ஺⌮C1S-1R⊤{⚪᝞+e,4ᑣᡃeᶇ஺c)᝞ᡃeA4ᡃeᡂ஺`EᡃeA஺Hᡃeᡂ஺E-H⌮ᣚCH-E⊤{⚪ᡃeᡂ4ᑣᡃeA஺⌮C1H--|E⊤{⚪ᡃᡂ4ᑣᡃA(5)KLP6Q,QⅾP஺KLx1¡⚪⌕£KL(P—Q)AQnP,`(PnQ)AQFT,¤iJ(PnQ)FT,QFT,ᦑᵫ஺Ḅ¥¦4|ᨵPFT஺ᡠ3(PnQ)/\QnPx2ᵫ§⚪@l4ᓽK((P—Q)AQ)¨P©nC஺((P-Q)AQ)-P«(((PAQ)V(-|PA-|Q))AQ)-P=(1((PAQ)V(-|PA-,Q))V-,Q)VPo(((-IPV-]Q)A(PVQ))V-(Q)VP

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ᙠ(B)஺(B)ᵨ1
-1P,~|Q,P,Q,P-Q,F,T,-I(P—Q),

19ᙠ(B)஺(B)ᵨ
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!ᙠ(B)஺ᵫ"#$ᵨ%&'()*+ᵨᙠ%&,ᐗḄ/0!1234(B)Ḅ/05ᐳ78&9:Ḅ/0ᦑ;--<9=>2?ᜓḄA92=ᨬCὶ(E஺F#$,-I<9=ᨬCὶ(EGHIP஺Qo-I(P-Q),ᦑJKL⚪/0Ḅὶ(᝞7ᵨ;,[<⊤QᑣSTᵨ<⊤Qᐸ⌮WX஺ᦑ;,[

20-IPo(PAPA……)-iPoPf(Pf(Pf...)ᡠᨵL⚪,ᐗᢣeT,ᑣfg0hiIF,jiIT,kfg⊤Q0lm஺ᡠn;o<,;8pZ;-<9=ᨬCὶ(஺-A(9)#$;-1-2?ᜓḄὶ(EG;-|<,;-2?ᜓḄὶ(E஺ᡠn;-I,<=ᨬCὶ(E஺cGHIP-QO-!(PQ),ᡠn;-!,<=>2?ᜓḄὶ(EG;-I<,;<9=>c2?ᜓḄὶ(Eᡠn;-I,<=ᨬCὶ(E஺w⚪1-7পzPA(P-Q)oPA(iPVQ)o(PA-iP)V(PAQ)PA(PfQ)o(PV(nQAQ))A(nPVQ)o(PV-iQ)A(PVQ)A(-1PVQ)ফza)(-1PAQ)-Ro-i(-1PAQ)VR

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220-1(-1PVQ)V(PVQ)=(PAiQ)V(PVQ)o(PVPVQ)A(iQVPVQ)c)-i(P-Q)(~iPVQ)oPA-iQ<=>(PVQ)A(PV-iQ)A(-1QV-iP)d)(PfQTo-i(-1PVQ)VR=(PA-iQ)VRo(PVR)A(-1QVR)e)(-1PAQ)V(PAnQ)0(1PVP)A(-1PV-iQ)A(QVP)A(QVnQ)0(1PV-iQ)A(QVP)za)(-1PV-iQ)-(P5|Q)(-|PV-iQ)VQ)o(PAQ)V(PAnQ)V(nPAQ)2.3oPVQ=n°b)QA(PV-1Q)o(PAQ)V(QAnQ)<=>PAQ=Z3

23^^rio,i,2^(PVQ)A(PVnQ)A(-1PVQ)c)PV(nP-(QV(-|Q-R))^>PV(PV(QV(QVR))^>PVQVR=n0o',2,3,4,5,6,7=(nPA-iQAR)V(nPAQA-iR)V(nPAQAR)V(PAQAnR)nV(PAnQAR)V(PAQA-|R)V(PAQAR)d)(P-(QAR))A(iP-(1QA-iR))o(-1PV(QAR))A(PV(nQA-iR))o(PA-jP)V(PA(QAR))V((-iQA-iR)AnP)V((nQA-jR)A(QAR))o(PAQAR)V(nPA-iQA-iR)=Zo.7Olli,2,3,45,6o(PVQV-1R)A(PV-1QVR)A(PVqQVnR)A(nPVQVR)A(nPVQV-iR)A(-1PV-iQVR)e)P-(PA(QfP)o-iPV(PA(-)QVP)o(iPVP)A(nPV-iQVP)oTV(TAiQ)oT=Z(u,2,3=(-1PA-iQ)V(-1PAQ)V(PA-iQ)V(PAQ)f)(Q-P)A(nPAQ)o(nQVP)A-iPAQo(nQVP)A-i(PV-iQ)oF

24<=>no,n2,3=(PVQ)A(PV-IQ)A(-1PVQ)A(iPVnQ)(5)#$:a)(A-B)A(A-*C)o(-1AVB)A(nAVC)A-*(BAC)biAV(BAOo(-1AVB)A(-1AVC)b)(A-*B)f(AAB)o-i(-1AVB)V(AAB)o(AA-iB)V(AAB)=AA(BV-iB)oAAToA(-1A-B)A(B-A)o(AVB)A(-1BVA)oAV(BAiB)oAVFoAc)AABA(nAV-iB)o((AA-iA)V(AA-iB))AB

25<=>AABA-iBoF-iAA-iBA(AVB)<=>((-)AAA)V(~iAAB))A-iB<=>nAA-!BAB<=>Fd)AV(A-(AAB)<=>AVnAV(AAB)oT-1AV-iBV(AAB)o-i(AAB)V(AAB)<=>T(6)z:AoRt(QA-i(RIP)),ᑣA*=RI(QVn(RfP))AoRt(QAn(RIP))o-i(RA(QA(RVP)))o-iRV-iQVn(RVP)o-i(RAQ)Vn(RVP)A*oRI(QVn(RtP))<=>-1(RV(QV(RAP))o-iRAnQAn(RAP)o-i(RVQ)An(RAP)(7)zAA஺BB஺CC஺DD஺

26[AᑣCZD⌕&஺A^(CVD)BZC92t஺-I(BAC)CᑣD⌕ᶇ஺C-τDᢥ⚪ᨵA-(CVD),(BAC),C--|DSᡂ஺HICWDo(CA-ID)V(DAn0ᦑ(A-(CVD))Ai(BAC)A(C-”)o(nAV(CA-iD)V(DAn0)An(BAC)A(nCVqD)o(-1AV(CA-iD)V(DAn0)A(nBVn0A(nCVnD)(-1AV(CA-iD)V(DAn0)A((-iBAn0V(nBAnD)V(nCAnD)Vn0o("iAA-iB/\~iC)V(~iAA-iD)\/(~iAA~iCB-iD)V(-|AA-iC)V(nBAnCAD)o(-!CAD/\iBAiD)V(iCADAiC8iD)V(nCADA-i0V(iDAC/X-iB8iC)V(nDACAnBAnD)V(iDACA-iC/\iD)V(-iDACA-i0ᙠ"¡Ḅ᪆£0ᨵ¥(¦§Ḅ)9¨ᔠ⚪ª«(-1AA-i0V(nBAnCAD)V"CAD)V(nDACAqB)ᦑᑖeḄ®IBAD,ᡈDAA,ᡈCAAo(8)zPA=°஺QB=°±஺R²C=°±஺SD=°³஺EA=°±஺ᵫ⚪(PVQ)A(RVS)A(EVS)஺((PA-iQ)V(nPAQ))A((RAnS)V(nRAS))A((EAS)V(nEAS))no((PA-iQARA-iS)V(PA-|QAqRAS)V(nPAQARAnS)V(nPAQA-iRAS))A((EAnS)V(nEAS))HI(P/\iQAiRAS)kJPAQARAiS)9ᔠ⚪ᡠnµ0TᓄI((PA-iQARA-iS)V(-iPAQA-iRAS))A((EA-|S)V(nEAS))

27a(PA-iQARA-iSAEAnS)V(PAnQARAqSAnEAS)V(nPAQA-iRASAEA-iS)V(nPAQAnRASAqEAS)o(PA-iQARA-iSAE)V(nPAQAnRASAnE)HRkElmᦑiPAQA-iRASAnEIXᓽA9=°B=°±C9=°±DI°³A9=°±஺¸=A=°¹B=°±C=°D=°³஺w⚪1-8প#$a)-|(PAnQ),"iQVR,nR=nP(1)-iRP(2)-iQVRP(3)-iQ(1)(2)T,I(4)-i(PA-iQ)P(5)-iPVQ(4)T,E(6)-iP(3)(5)T,Ib)J-(MVN),(HVG)-J,HVG^MVN(1)(HVG)fJP(2)(HVG)P(3)JপফT,I(4)J-(MVN)P(5)MVN(3)(4)T,Ic)BAC,(B6C)-(HVG)nGVH

28(1)BACP(2)B(1)T,I(3)C(1)T,I(4)BV-iC(2)T,I(5)CV-iB(3)T,I(6)C-B(4)T,E(7)BfC(5)T,E(8)BcC(6)(7)T,E(9)(BcC)-(HVG)P(10)HVG(8)(9)T,Id)PfQ,(-)QVR)A-iR,(-iPAS)=>-|S(1)(-1QVR)AnR(2)-iQVR(1)T,I(3)-iR(1)T,I(4)-iQ(2)(3)T,I(5)P-QP(6)-iP(4)(5)T,I(7)-i(-1PA-iS)P(8)PV-iS(7)T,E(9)-iS(6)(8)T,Iফ#$a)-iAVB,Cf-iB=Af-|C(1)-i(Af-|C)P

29(2)A(1)T,I(3)C(1)T,I(4)-|AVBP(5)B(2)(4)T,I(6)C-iBP(7)-|B(3)(6)T,I(8)BA-iBlm஺(5),(7)b)A-(BfC),(CAD)fE,-1Ff(DA-iE)nA—(BfF)(1)-i(A-(BfF))P(2)A(1)T,I(3)-i(B-F)(1)T,I(4)B(3)T,I(5)-iF(3)T,(6)Af(BY)P(7)BfC(2)(6)T,I(8)C(4)(7)T,I(9)-iF-(DA-|E)P(10)DA-iE(5)(9)T,I(11)D(10)T,I(12)CAD(8)(11)T,I(13)(CAD)fEP(14)E(12)(13)T,I(15)-iE(10)T,I

30(16)EA-iElm஺(14),(15)c)AVB^CAD,DVEfFnA-F(1)-i(A-F)P(2)A(1)T,I(3)-iF(1)T,I(4)AVB(2)T,I(5)(AVB)-CADP(6)CAD(4)(5)T,I(7)C(6)T,I(8)D(6)T,I(9)DVE(8)T,I(10)DVE-FP(11)F(9)(10)T,I(12)FA-iFlm஺(3),(11)d)A-(BAC),nBVD,(E-iF)-iD,B-(AA-|E)nB-E(1)-i-E)P(2)B(1)T,I(3)-iE(1)T,I(4)-|BVDP(5)D(2)(4)T,I(6)(E-τF)DP(7)-)F)(5)(6)T.I(8)E(7)T,I

31(9)EA-iElme)(A-B)A(CfD),(B-E)A(D-F),(EAF),A-C=>Ann(1)(A-B)A(C-*D)P(2)A-BপT,I(3)(B-E)A(D-F)P(4)B-E(3)T,I(5)A-E(2)(4)T,I(6)-i(EAF)P(7)-|EV-iF(6)T,E(8)EiF(7)T,E(9)A--|F(5)(8)T,I(10)C-D(1)T,I(11)D-F(3)T,I(12)CfF(10)(10)T,I(13)A-CP(14)A-F(13)(12)T,I(15)-iF-*nA(14)T,E(16)Af-iA(9)(15)T,I(17)AV-iA(16)T,E(18)-iA(17)T.Eব#$a)nAVB,Cf-iB=>Af-]C(1)AP

32(2)-|AVBP(3)B(1)(2)T,I(4)CfBP(5)-iC(3)(4)T,I(6)A--|CCPb)Af(B-C),(CAD)-E,Ff(DA-|E)(B-F)(1)AP(2)Af(B-C)P(3)B-C(1)(2)T,I(4)BP(5)C(3)(4)T,I(6)(CAD)fEP(7)C-(D-E)(6)T,E(8)D-E(5)(7)T,I(9)-iDVE(8)T,E(10)-i(DA-iE)(9)T,E(11)-iF-(DA-iE)P(12)F(10)(11)T,I(13)B-FCP(14)A-(B-*F)CPc)AVB-CAD,DVEfFnA-F(1)AP(2)AVBপT,I

33(3)AVB^CVDP(4)CAD(2)(3)T,I(5)D(4)T,I(6)DVE(5)T,I(7)DVE^FP(8)F(6)(7)T,I(9)A-FCPd)Af(BAC),BVD,(E-iF)—|D,B-(AAiE)nB-E(1)BP(▬ÁÂÃ)(2)-|BVDP(3)D(1)(2)T,I(4)(Ef[F)-*-iDP(5)-i(Ef-iF)(3)(4)T,I(6)E(5)T,I(7)BfECPভ#$a)Rf-iQ,RVS,S-,—|Q,PfQn-jP(1)R-iQP(2)RVSP(3)Sf-iQP(4)Q(1)(2)(3)T,I(5)P-QP(6)-iP(4)(5)T,I

34b)Sf-iQ,SVR>_iR,P—QnP#®(1)SVRPফ1RP(3)S(1)(2)T,I(4)S-iQP(5)-iQ(3)(4)T,I(6)-iPoQP(7)(iP-Q)A(Qf-iP)(6)T,E(8)nP-Q(7)T,I(9)P(5)(8)T,I#®±()#®)(1)1PP(▬ÁÂÃ)(2)nP3P(3)(-1P-Q)A(Q-iP)(2)T,E(4)-iP-*Q(3)T,I(5)Q(1)(4)T,I(6)S-iQP(7)S(5)(6)T,I(8)SVRP(9)R(7)(8)T,I(10)-iRP(11)-|RARlm(9)(10)T,I

35c)-|(PfQ)f-i(RVS),((QfP)V-iR),RnP-Q(1)RP(2)(QfP)V-iRP(3)Q-*P(1)(2)T,I(4)-1(P-Q)(RVS)P(5)(RVS)f(P-Q)(4)T,E(6)RVS(1)T,I(7)P-Q(5)(6)(8)(P-Q)A(Q-P)(3)(7)T,I(9)P6Q(8)T,Eমza)PᡃÈÉ஺QᡃÊËÌ஺ÂÃIPfQ,~1Q(1)P-QP(2)-iQP(3)-iP(1)(2)T,IÍIÎP,ᡃÏᨵÈÉ஺b)SÐÑÒ┯Ô஺RÐÕ⁐×Ø஺ÂÃIS-R,RHI(SfR)ARo(-1SVR)8RoR஺ᦑÙ⚪ÏᨵÚÛḄÍ஺Ü▭"[S-RIXRIXᑣSTIXSYTIᎷᦑßᨵᦔÍ஺c)PᡃḄáâãä஺QᡃÊåæ஺R□ᐝÊé஺SᜩÊᨨZ஺ìíî"ᓝðᳮzI□ᐝ9éò

36ÂÃIPfQ,Q-R,-iRAS(1)P-QP(2)Q-RP(3)P-R(1)(2)T,I(4)-iRVSP(5)-iR(4)T,I(6)-iP(3)(5)T,IÍI1P,ᡃḄáâÏᨵãäw⚪2-1,2-2(1)za)W(x)x=õö஺cCØ஺ᑣᨵ7(c)b)S(X)x=ᵪù
úᕒ஺B(X)x=ᳫ
úᕒ஺hÐᑣᨵS(h)vB(h)c)C(x)x=ÿḄ஺B(x)xḄ஺1⃅஺ᑣᨵC(1)B(1)d)0(X)x᜻ᦪ஺ᑣᨵ0(m)0(2m)oe)R(x)xᦪ஺Q(x)xᨵᳮᦪ஺ᑣᨵ(Vx)(Q(x)-R(x))f)R(X)xᦪ஺Q(x)xᨵᳮᦪ஺ᑣᨵGx)(R(x)AQ(x))

37g)R(x)xᦪ஺Q(x)xᨵᳮᦪ஺ᑣᨵ'(Vx)(R(x)-Q(x))h)P(x,y),-x./0,-yG(x,y),-x120,-y஺ᑣᨵP(A,B)3->G(A,B)(2)5:a)J(x)xᦟ:ᕒ஺L(x)x=>ᕒ஺ᑣᨵ(X/x)(J(x)fL(x))b)S(x)xᜧCD஺L(x)x=>ᕒ஺ᑣᨵ(3x)(L(x)AS(x))c)J(x)xᦟ:ᕒ஺0(x)xGὁḄ஺V(x)xᏉJḄ஺ᑣᨵ(3x)(J(x)AO(x)AV(x))d)0(x)xGὁḄ஺V(x)xᏉJḄ஺jLᦟ:ᑣᨵ'0(j)V(j)e)L(x)x=>ᕒ஺J(x)xᦟ:ᕒ஺ᑣ'(Vx)(L(x)Tj(x))N⚪PQᳮ5RST=>ᕒUᦟ:஺ᦑGx)(L(x)A-IJ(x))f)S(x)xᜧCD஺L(x)x=>ᕒ஺C(x)xWX⌱Z஺ᑣᨵ(3x)(S(x)AL(x)AC(x))g)C(x)xWX⌱Z஺V(x)xᏉJḄ஺ᑣᨵ(Vx)(C(x)fV(x))ᡈ'Gx)(C(x)AIV(x))h)C(x)xWX⌱Z஺0(x)xὁḄ஺L(x)x=>ᕒ஺

38ᑣᨵ(Vx)(0(x)AC(x)->L(x))i)W(x)x᝕_`஺H(x)xXbᝣ᝕஺C(x)xWX⌱Z஺ᑣᨵdGx)(W(x)AC(x)AH(x))j)W(x)x᝕_`஺J(x)xᦟ:஺C(x)xWX⌱Z஺ᑣᨵGx)(W(x)AJ(x)AC(x))k)L(x)x=>ᕒ஺J(y)yᦟ:஺A(x,y)xfgy஺ᑣᨵ(Vx)(L(x)->(3y)(J(y)AA(X,y)))1)S(x)xᜧCD஺L(x)x=>ᕒ஺A(x,y)xfgy஺ᑣGx)(S(x)A(Vy)(L(y)->-iA(x,y)))h⚪2-3(1)5:a)5jᦪ஺b)2Ꮤᦪl2jᦪ஺c)mᡠᨵḄx,oxpq2◀stᑣxᏔᦪ஺d)uᙠx,xᏔᦪ,lxp◀s6஺(ᓽSTᏔᦪp◀s6)e)mᡠᨵḄx,oxUᏔᦪtᑣxUpq2◀s஺f)mᡠᨵḄx,oxᏔᦪtᑣmᡠᨵḄy,oxp◀sy,ᑣyyᏔᦪ஺g)mᡠᨵḄx,oxjᦪtᑣuᙠy,yᏔᦪlxp◀sy(ᓽᡠᨵjᦪp◀sSTᏔᦪ)஺h)mᡠᨵḄx,ox᜻ᦪtᑣmᡠᨵy,yjᦪtᑣxUp◀sy(ᓽz{᜻ᦪUp◀sz{jᦪ)஺(2)5(Vx)(Vy)((P(x)AP(y)A-E(x,y)-0!z)(L(z)AR(x,y,z)))1

39ᡈ(Vx)(Vy)((P(x)AP(y)AnE(x,y)(3z)(L(z)AR(x,y,z)An(3u)(nE(z,u)AL(u)AR(x,y,u))))(3)5a)N(x):xᨵ▲ᦪḄ஺z(y):yR0஺P(x):xḄR஺F(y):yḄ஺ᑣᨵ(Vx)((N(x)AP(x)->(3y)(F(y)Az(y)))b)R(x):xᦪ஺Q(x,y):yᜧ0x஺ᦑ(Vx)(R(x)^(3y)(Q(x,y)AR(y)))c)R(x):xᦪ஺G(x,y):xᜧ0y஺ᑣ(3x)(3y)(3z)(R(x)AR(y)AR(z)AG(x+y,xz)(4)5G(x,y):xᜧ0y஺ᑣᨵ(Vx)(Vy)(Vz)(G(y,x)AG(0,z)-*G(xz,yz))(5)5N(x):xᦪ஺S(x,y):yxḄᦪ஺E(x,y)x=y.ᑣa)(Vx)(N(x)->(3!y)(N(y)AS(x,y)))ᡈ(Vx)(N(x)-0y)(N(y)S(x,y)An(3z)(E(y,z)AN(z)AS(x,z))))nb)n(3x)(N(x)AS(x,l))c)(Vx)(N(x)AnS(x,2)-(3!y)(N(y)AS(y,x)))ᡈ(Vx)(N(x)AiS(x,2)->(3y)(N(y)AS(y,x)An(3z)(E(y,z)AN(z)AS(z,x))))n(6)5S(x):xᜧCD஺E(x):xᡚḄ஺F(x):xᵨḄ஺R(x,y):xᙠy஺G(y)yᜧḄ஺K(y):yḄ஺J(y):y℉஺a:N஺b¡¢஺ᑣᨵE(b)AF(b)AS(b)AR(b,a)AG(a)AK(a)AJ(a)(7)5P(x,y):xᙠy¤¥஺Q(x,y):x>yᑣoP(f,a)^((V)(35)(Vx)(Q(8,0)->(Q(5,0)AQ(5)|x-a|)-Q(8,|f(x)-f(a)|))))e

40h⚪2-4(1)5a)x¨©ªᐗty¬ᵫªᐗ஺b)x¨©ªᐗtP(x)AQ(x)Ḅx®ᐰ°±²VḄ¨©tS(x)Ḅx®uᙠ±²³Ḅ¨©஺c)x,y´¨©ªᐗ,P(x)Ḅx®³Ḅ¨©tR(x)Ḅx®VḄ¨©஺d)x,y¨©ªᐗtz¬ᵫªᐗ஺(2)5a)P(a)AP(b)AP(c)b)R(a)AR(b)AR(c)AS(a)AS(b)AS(c)c)(P(a)-Q(a))A(P(b)-Q(b))(P(c)-Q(c)d)(-|P(a)A-IP(b)A-|P(c))V(P(z)AP(b)AP(c))e)(R(a)AR(b)AR(c))A(S(a)VS(b)VS(c))ব5a)(Vx)(P(x)VQ(x))«(P(l)VQ(l))A(P(2)VQ(2)),¶PপRT,QপRRP(2)RF,Q(2)RT,ᡠ¸(Vx)(P(x)VQ(x))o(TVF)A(FVT)oT஺b)(Wx)(P-Q(x))VR(a)o((P-Q(—2))(P-Q(3))(P-Q(6)))VR(a)RPRT,Q(—2)RT,Q(3)RT,QযRF,R(5)RF,ᡠ¸(Vx)(P-Q(x))VRXa)o((T—T)A(T-T)(T-F))VFoF(4)5a)(Vu)(3v)(P(u,z)1Q(v)ᓲS(x,y)b)(Vu)(P(u)ߟ(R(u)VQ(u))A(3v)R(v))^(3z)S(x,z)(5)5a)((3y)A(u,y)"x)B(x,v))A(3x)(Vz)C(x,t,z)b)((Vy)P(u,y)A(3z)Q(u,z))V(Vx)R(x,t)

41h⚪2-5প5:a)P(a,f(a))AP(b,f(b))oP(1,f(l))AP(2,f(2))oP(1,2)AP(2,1)oTAFoFb)(Vx)(3y)P(y,x)«(Vx)(P(l,x)VP(2,x))o(P(l,l)VP(2,1))A(P(1,2)VP(2,2))^(TVF)A(TVF)oTc)(Vx)(Vy)(P(x,y)->P(f(x),f(y)))O(Vx)((P(x,l)->P(f(x),f(l)))A(P(x,2)-P(f(x)f(2))))o(P(1,1)P(f(1),f(1)))A(P(1,2)-P(f(1),f(2)))A(P(2,l)->P(f(2),f(l)))A(P(2,2)-P(f(2),f(2)))=(P(1,1)P(2,2))(P(1,2)-P(2,1))A(P(2,1)P(1,2))(P(2,2)-P(1,1))o(T-FA(T—F)A(F—T)A(F-T)oFAFATATOF(2)5a)(Vx)(P(x)-Q(f(x),a))o(Pপ-Q(f(1),1))A(P(2)-Q(f(2),1))O(F-Q(2,1))A(TTQ(1,1))u>(F-F)A(T-T)oTb)(3x)(P(f(x))AQ(x,f(a))o(P(f(1))AQ(1,f(1)))V(P(f(2))AQ(2,f(1))«(TAT)V(FAF)OTc)(3x)(P(x)AQ(x,a))o(PপAQ(l,a))V(PফAQ(2,a))=(PপAQ(1,1))V(PফAQ(2,1))o(FAT)V(T/\F)oFd)(Vx)(3y)(P(x)AQ(x,y))<=>(Vx)(P(x)A(3y)Q(x,y))o(Vx)(P(x)A(Q(x,l)VQ(x,2)))

42=(P(1)A(Q(1Á)VQ(1,2)))A(P(2)A(Q(2,1)VQ(2,2)))(FA(TVT))A(TA(FVF))oF(3)ÂÃÄÅᑡᔜⅾÉÊ஺a)[(0x)(P(x)Q(a))n(3x)P(x)^lQ(a)b)(Vx)(lP(x)-Q(x)),(Vx)[Q(x)nP(a)c)(Vx)(P(x)-Q(x)),(Vx)(Q(x)fR(x))n(Vx)(P(x)-R(x))d)(Vx)(P(x)vQ(x)),(Vx)lP(x)=>0X)Q(X)e)(Vx)(P(x)vQ(x)),(Vx)]P(x)n(Vx)Q(x)5a)R](0x)(P(x)Q(a))u>[0x)P(x)V]Q(a)ᦑËÊR10x)P(x)V]Q(a)n(3x)P(x)->lQ(a)P(x)xᜧCD஺Q(x)x=>ᕒÌÍᡈὅUuᙠx,xᜧCDtᡈὅa=>ᕒÏÐ᝞ÒuᙠxᜧCDtᑣÓᨵa=>ᕒ஺b)P(X)xẆÕD஺Q(X)xᜧCD஺aÐÖḄS×஺ÌÍmÐÖᡠᨵx,᝞ÒxUẆÕDᑣxᜧCD஺mÐÖᡠᨵx,xUᜧCD஺ÏÐmÐÖᡠᨵx´ẆÕD஺ᦑtmÐÖSa,ÓᨵÏÐaẆÕDtᓽP(a)ᡂÙ஺c)P(x)xẆÕD஺Q(X)xÚÛÜᜧC஺R(x)xÚÛÜC஺ÌÍmᡠᨵx,᝞ÒxẆÕDtᑣxÚÛÜᜧC஺mᡠᨵx,᝞ÒxÚÛÜᜧCtᑣxÚÛÜC஺ÏÐmᡠᨵx,᝞ÒxẆÕDtᑣxÚÛÜC஺d)P(x)xẆÕD஺Q(X)x=>ᕒ஺

43ÌÍmᡠᨵX,ᡈὅXẆÕDtᡈὅX=>ᕒ஺mᡠᨵX,XUẆÕDÏÐÓuᙠX,X=>ᕒ஺e)P(x)xẆÕD஺Q(X)x=>ᕒ஺ÌÍmᡠᨵx,ᡈὅxẆÕDtᡈὅx=>ᕒ஺mᡠᨵX,XUẆÕDÏÐmᡠᨵX,X=>ᕒ஺(4)Ý0x)(A(x)fB(x))o0x)(iA(x)VB(x))o0x)-|A(x)V(3x)B(x)o-|(Vx)A(x)V(3x)B(x)(Vx)A(x)->(3x)B(x)(5)ÐÖD={a,b,c},ÞÝ(Vx)A(x)D(Vx)B(x)n(Vx)(A(x)VB(x))ÝRÐÖß=¶tb,c},ᡠ¸(Vx)A(x)V(Vx)B(x)<=>(A(a)AA(b)AA(c))V(B(a)AB(b)AB(c))0(A(a)VB(a))A(A(a)VB(b))A(A(a)VB(c))A(A(b)VB(a))A(A(b)VB(b))A(A(b)VB(c))A(A(c)VB(a))A(A(c)VB(b))A(A(c)VB(c))n(A(a)VB(a))A(A(b)VB(b))A(A(c)VB(c))=(Vx)(A(x)VB(x))ᡠ¸(Vx)A(x)V(X/x)B(x)n(Vx)(A(x)VB(x))(6)5àÝUáâtR-1(3x)(A(x)Anãx))oi((3x)A(x)A(3x)B(x))n(7)ÞÝ(Vx)(Vy)(P(x)fQ(y))o(3x)P(x)-*(Vy)Q(y)Ý(Vx)(\/y)(P(x)fQ(y))=(Dx)(Vy)(-iP(x)VQ(y))O(Vx)iP(x)V(Vy)Q(y)

44=1(3x)P(x)V(Vy)Q(y)o(3x)P(x)-*(Vy)Q(y)h⚪2-6(1)5a)(Vx)(P(x)-*(3y)Q(x,y))o(Vx)(iP(x)V(3y)Q(x,y))=(X/x)0y)(iP(x)VQ(x,y))b)(3x)((0y)P(x,y))—(0z)Q(z)fR(x)))n^(3x)((3y)P(x,y)V((3z)Q(z)->R(x)))<=>(3x)((3y)P(x,y)V(n(3z)Q(z)VR(x)))=0x)(0y)P(x,y)V((Vz)-|Q(z)VR(x)))<^(3x)(3y)(Vz)(P(x,y)VnQ(z)VR(x))c)(Vx)(Vy)(((3zP(x,y,z)A(3u)Q(x,u))—(3v)Q(y,v))o(Vx)(Vy)(i((3z)P(x,y,z)A(3u)Q(x,u))V(3v)Q(y,v))<^>(Vx)(Vy)((Vz)-|P(x,y,z)V(Vu)nQ(x,u)V(3v)Q(y,v))«(Vx)(Vy)((Vz)-|P(x,y,z)V(Vu)nQ(x,u)V(3v)Q(y,v))<^(Vx)(Vy)(Vz)(Vu)(3v)(nP(x,y,z)ViQ(x,u)VQ(y,v))(2)5:a)((3x)P(x)V(3x)Q(x))->(3x)(P(x)VQ(x))01((3x)P(x)V(3x)Q(x))V(3x)(P(x)VQ(x))=1(3x)(P(x)VQ(x))V(3x)(P(x)VQ(x))<=>Tb)(Vx)V(x)—(Vy)((Vz)Q(x,y)fÁ(Vz)R(y,x)))o(Vx)(-iP(x)V(Vy)(Q(x,y)->-]R(y,x)))o(Vx)(Vy)(-|p(x)VnQ(x,y)VnR(y,x))

45Ì©ᔠåÊo(Vx)(Vy)((P(x)AQ(x,y)AR(y,x))V(P(x)AQ(x,y)AnR(y,x))V(P(x)A-iQ(x,y)AR(y,x))V(nP(x)AQ(x,y)AR(y,x))V(nP(x)A-iQ(x,y)AR(y,x))V((P(x)AnQ(x,y)A-iR(y,x))V(-iP(x)AQ(x,y)AnR(y,x)))Ì©᪆åÊc)(Vx)P(x)-*(3x)((Vz)Q(x,z)V(Vz)R(x,y,z))<=>-|(Vx)P(x)V(3x)((Vz)Q(x,z)V(Vz)R(x,y,z))=0x)1P(x)V(3x)((Vz)Q(x,z)V(Vu)R(x,y,u))=0X)(1P(x)V(Vz)Q(x,z)V(Vu)R(x,y,u))<=>(3x)(Vz)(Vu)(nP(x)VQ(x,z)VR(x,y,u))Ì©ᔠåÊ<=>(3x)(Vz)(Vu)((P(x)AQ(x,z)AR(x,y,u))V(P(x)AQ(x,z)AnR(x,y,u))V(P(x)AnQ(x,z)AR(x,y,u))V(P(x)AnQ(x,z)AnR(x,y,u))V(nP(x)AQ(x,z)AnR(x,y,u))V(nP(x)AnQ(x,z)AR(x,y,u))V(nP(x)AnQ(x,z)AnR(x,y,u)))Ì©᪆åÊ

46d)(Vx)(P(x)->Q(x,y))->((3y)P(y)A(3z)Q(y,z))o-i(Vx)(iP(x)VQ(x,y))V((3y)P(y)A(3z)Q(y,z))=0x)(P(x)AnQ(x,y))V((3u)P(u)A(3z)Q(y,z))<^(3x)(3u)(3z)((P(x)AnQ(x,y))V(P(u)AQ(y,z)))Ì©᪆åÊO0X)0u)0z)((P(x)VP(u))A(P(x)VQ(y,z))A(nQ(x,y)VP(u))A(nQ(x,y)VQ(y,z)))Ì©ᔠåÊh⚪2-7(1)Ý(2)aXD(Vx)(iA(x)fB(x))Pঝ-1A(u)-B(u)USজঞ(Vx)B(x)Pnট1B(u)USঞঠA(u)VB(u)TঝEডA(u)TটঠIঢ(3x)A(x)EG@b)G>i(Vx)(A(x)fB(x))P(▬ðÌÍ)3x)-|(A(x)fB(x))TজEঞ1(A(c)-B(c))ESঝ@A(c)TঞIঠ1B(c)TঞI

47(6)(3x)A(x)EGটঢ0x)A(x)f(Vx)B(x)Pণ(Vx)B(x)TডঢIতB(c)USণথB(c)-|B(c)Tঠতòóc)©(Vx)(A(x)->B(x))PঝA(u)fB(u)USজ@(Vx)(C(x)-*-|B(x))pটC(u)-iB(u)USঞঠ1B(u)~iA(u)TঝEডC(u)~*A(u)TটঠIঢ(Vx)(C(x)f-iA(x))UGডd)(Vx)(A(x)VB(x)),(Vx)(B(x)f-|C(x)),(Vx)C(x)n(Vx)A(x)@(Vx)(B(x)fC(x))PঝB(u)-iC(u)USজ(3)(Vx)C(x)P@C(u)USঞঠ1B(u)TঝটI@(Vx)(A(x)VB(x))PঢA(u)VB(u)USণA(u)TঠঢIত(Vx)A(x)UGণ(2)Ý:

48a)®(Vx)P(x)P(▬ðÌÍ)ঝP(u)USজঞ(Dx)(P(x)-Q(x))PটP(u)-Q(u)USঞঠQ(u)TঝটIড(Vx)Q(x)UGঠôVx)P(x)->(Vx)Q(x)CPb)R"x)P(x)V0x)Q(x)=-i(Vx)P(x)f0x)Q(x)ᦑN⚪õàÝ(Vx)(P(x)VQ(x))=>-|(Vx)P(x)fQx)Q(x)জ-I(Vx)P(x)Pö▬ðÌÍ÷@(3x)-|P(x)TজEঞ1P(c)ESঝ@(Vx)(P(x)VQ(x))PঠP(c)VQ(c)ES@ডQ(c)TঞঠIঢ(᝕)Q(x)EGডণ1(Vx)P(x)-*(3x)Q(x)CP(3)5a)R(x)xᦪ஺Q(x)xᨵᳮᦪ஺I(x)x᦮ᦪ஺N⚪úûᓄR(Vx)(Q(x)-R(x))A(3x)(Q(x)Al(x))=>(3x)(R(x)Al(x))জ0x)(Q(x)Al(x))PঝQ(c)A1(c)ESজ

49ঞ(Vx)(Q(x)-R(x))P@Q(c)fR(c)USঞঠQ(c)TঝI@R(c)TটঠIঢ1(c)TঝIণR(c)Al(c)TডঢI©(3x)(R(x)Al(x))EGণb)P(x)xýþÿ஺Q(x)x஺R(x)x⚪ᓄ(Vx)(P(x)f-jQ(x)),(Vx)(Q(x)VR(x)),(3x)R(x)=>(3x)P(x)nnজQx)-iR(x)Pঝ-IR(c)ESজঞ(Vx)(Q(x)VR(x))P@Q(c)VR(c)USঞঠQ(c)TঝটI@(Vx)(P(x)Q(x))PঢP(c)-Q(c)USডণ-1P(c)TঠঢIত0x)-iP(x)EGণc)ᜧᦻ!"ᳮ$!%ᨵḄᜧ()%*+ᳮ$!%,-()%./᝞1*+ᜧ%-"ᦻ!஺2G(x)xᜧ஺L(x)xᦻ!஺P(x)xᳮ$!஺S(X)x(5஺c*+஺

50⚪ᓄ(Vx)(G(x)-L(x)VP(x)),(3x)(G(x)AS(x)),P(c),S(c)=>G(c)T(c)nজG(c)P(▬789)ঝ(Vx)(G(x)-L(x)VP(x))PঞG(c)fL(c)VP(c)USঝ@L(c)VP(c)TজঞIঠ1P(c)PডL(c)TটঠI©G(c)fL(c)CP:;:⚪=>?@ABᵨᑮ890x)(G(x)AS(x))EFS(c)஺G⌕S(x)x(5%IᩩKLᐸ-89ḄὶOP>QRSTᨵUV%.S(x)Lᐸ-89WX,ᦑ⚪Ḅ=>[ᨵᦔḄ஺

513-5.1ᑡ^ᡠᨵ`X={a,b,c}aIbY={s}ḄᐵO஺dL={<1,2>,<1,3>,<1,6>,<2,3>,<2,6>,<3,6>,<1,1>,<2,2>,<3,3>,<6,6>}dZ1={)D={<1,2>,<1,3>,<1,6>,<2,6>,<3,6>,<1,Z={}1>,<2,2>,<3,3>,<6,6>)2Z={}LAD=3e={,}{<1,2>,<1,3>,<1,6>,<2,6>,<3,6>,<1,1>,Z={,}<2,2>,<3,3>,<6,6>)5Z6={,}Z={,,}35.5P¶ᑡ¦·%¸^AlḄuᐗ7ᐵO%¹¸^ᐵOº3-5.2ᙠ♦ᨵnᐗiḄjᔠl%ma){|0^xAy^3},I»EᨵnopqḄᐵO஺A={1,2,3,4}¼b){|2x,7½x◀¾y,Id.ᙠXAḄstuᐗᐵOvX»A={n|neNAn^lO}XXḄwj%/XXX=X?AᐳᨵMc){|0^x-y<3},I»ᐗi%y0ᑮMᐗi%ᐳmzA={0,1,2,3,4}¼d){vx,y>|x,y¿ÀḄ},I»ᡂ2"‘wj%ᓽ}(XxX)|=2"ஹA={2,3,4,5,6}3-5.32={600,630,730,…%930,1030}⊤ᙠl◞*dḄḄjᔠ,2B={3,12,15,17}a)R={<0,0>,<0,1>,<0,2>,<0,3>,⊤ᙢᵯ⚣⍝Ḅjᔠ%2RiR2`AᑮBḄuᐔᐵO%P<2,0>,<2,1>,<2,2>,<2,3>,uᐵORi%R2,RIUR2,RiCIR2,<3,0>,<3,1>,<3,2>,<3,3>,}R1೙RR1-R2mᑖ^᪵ḄdᐸᐵOº2஺dAXB⊤ᙠlᵯ⚣⍝ᡠzᡂḄᵯ⁚⊤஺RiR2ᑖAXBḄwj%᝞*⊤⁚^Ḅ⊤%R¡¢⁚£Ḅ^⊤%ᑣRiU2R⊤ᡈ¡¢⁚Ḅ^2⊤%RiCR2⊤¡¢¦§^Ḅ⊤%Ri೙R?⊤⁚⊤EF¡¢⁚⊤%,¡¢¦§Ḅ⁚¨⊤%RI-R2⊤¡¢Ḅ⁚©஺b)R={<2,0>,<2,2>,<2,4>,<2,6>,<3,0>,<3,3>,<3,6>,3-5.42L⊤ᐵO“*ᡈ)“%D<4,0>,<4,4>,⊤'᦮◀”ᐵO,LDᑐᙳ±²<5,0>,<5,5>,{1,2,3,6},ᑖᑏ^LDḄᡠᨵᐗ<6,0>,<6,6>,i´µ^LPD.<7,0>,<7,7>}

523-6.1ᑖ᪆jᔠ={1,2,3}lḄ¶ÉRmá⌴ḄḄÝPßḄ,òÊᐵOÝḄPßḄ஺(1)R={<1,1>,<1,2>,<1,3>,<3,3>)¼3-6.3ó^A={1,2,3}lᐵORḄ(2)S={<1,1>,<1,2>,<2,w%ôᐸᐹᨵ¶ÉឋÀ1>,<2,2>,<3,3>}¼a)÷PßḄ%øÝPßḄ¼(3)T={<1,1>,<1,2>,<2,b)R÷PßḄ%øÝPßḄ¼2>,<2,3>}¼c)Rmá⌴Ḅ஺(4)0=ÒᐵO;(5)AXAuᐰØᐵO஺dᑨÚAAḄlÉᐵOᔲa)ÝḄ%a)R={VI,1>,<2,2>,<3,3b)PßḄ%c)má⌴Ḅ%d)ÝPß>)Ḅ஺b)R={<1,2>,<2,1>,<2,3>)d(1)Rmá⌴ÝPßḄ஺c)R={<1,2>,<2,1>,<1,1(2)SÝ%Pßmá⌴Ḅ஺>,<2,2>,<3,3>}(3)TÝPßḄ஺(4)ÒᐵOPß%má⌴ÝPß3-6.4᝞1ᐵORSÝḄ%PḄ஺ßḄmá⌴Ḅ%>QRASúÝ%(5)ᐰØᐵOÝ%Pßmá⌴Pßmá⌴Ḅ஺Ḅ஺>Q2RSXbuḄòÝḄ%Pß3-6.2¸±A={1,2,3,4},ὃ⇋aIuḄmá⌴ḄᐵO஺ḄᐵOR,ç1^={<1,3>,<1,4>,1)Ps;x£X,ᨵVx,x>£RV<2,3>,<2,4>,<3,4>}x,x>GS,ᡠEVx,x>GRAS,a)ᙠAxAḄᙶ᪗ºl᪗^R,´ì^ᓽRASᙠX¦lòÝḄ஺íḄᐵOº2)Ps;ḄVx,y>GRnS,ᨵVx,b)Ri)ÝḄii)PßḄiii)máy>eRAes,RS⌴Ḅ%iv)ÝPßḄᔩñḄᦑᨵVy,x>GRAeSoᓽVy,x>eRDS,ᡠRCSᙠXḄ஺3)$%ḄVx,y>eRHSAeRns,ᑣᨵGRAGSA£RAesRS+⌴Ḅᦑ-Vx,z>eRAes,ᓽVx,z>GRnS,ᡠRCSᙠX+⌴Ḅ஺3-6.523S={1,2,3,4}Sᐵ;,<4,3>,<2,2>,<2,1>,<3,1>}=>R?@+⌴ḄABᐵ;R=R,C-ᓃ@+⌴ḄEFABG•I

533-7.1KRRzAḄ$%ᐵ;>es,xVy,z>eSo=>L.M⚪ḄOᎷQRS>஺VS+⌴ḄVx,z>£S,ᡠzSoSUaUVRR2WXḄᑣR஺YZCSoWXḄ[bUVRR2XWXḄᑣRoR?ZXKzSoSUaS,Ꮇ3Vx,y>XWXḄ[ESxVy,z>GS,ᑣVx,z>eSoS1,cUVRiYḄᑣRotZzSoSUcS,ᦑVx,z>QS,-Ḅ[ᑮS+⌴Ḅ஺dUVRY+⌴ḄᑣRotZ+⌴Ḅ஺bUKSWXḄVx,y>Glx,ᑣx=y஺lVx,x>GS,Vx,y证明反的aU$%a^A,KRR2W>=ES,-Ix=S஺所以,ᑣVa,a>eR,,^R2自反,eRlOR2,ᓽR9R2ZXIxcS,K$%x^X,eI,ᦑVx,x>GS,SWXXḄ஺bUᎷ஺f᝞}kR2={Vb,a>}cUKSXḄ஺Ꮇ3Vx,y>RiR2XWXḄ஺lR9R2={Va,asnsc,ij>},ᡠR9R2ᙠA?XWXḄ஺Vx,y>AGS'=Vx,y>GSAescUᎷ஺f᝞,Vb,a>,Vc,c>},ᡠVx,y>=Vx,x>elx,ᓽSCR2={,Vc,b>}SccIoXRR2ḄlRioRz={Va,c>,Vc,b>}XVSCSlx,KVx,y>6SxᡠR9R2?Ḅ஺Vy,x>£S,UeSAeScdUᎷ஺f᝞esnscRj{Va,b>,Vb,c>,Va,c>},=>IxR2={,,}ᦑ=ᓽSXḄ஺ᑣ%,ᵩr+⌴Ḅ஺lR9R2={Va,c>,Va,a>,}3-7.3KSXḄᐵ;S>VSᡠRoRz?+⌴Ḅ஺WX+⌴ḄISoS=S,ᐸ⌮Oᔩ3-7.2S>VSsᔠXḄuᐗᐵ;VSX+⌴ᐵ;ᵫ⚪aUS+⌴ḄwxywzSoSUcS[3-7.2aU@nzSoSU=S,bUSWXḄwxywIgS[Vx,y>es,᪷XឋᨵVcUS>3ᳮ3-7.3zbUzᓽSXx,x>es,ᨵVx,y>eSoS,Ḅwxywsns'uixU஺ᓽScSoSo-ljS=SoS.S>aUKS+⌴ḄVVx,z>I3ᳮḄ⌮?O஺f᝞X={L2,3},CSoS,ᑣᙠIy^X,C-Vx,yS={VI,2>,<2,2>,<1,1>},

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