离散数学(耿素云习题解)

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ᦣᦪ⚪Wind&MoonPressCanton,2008.2
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ᦣᦪ⚪2;<=⚪1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31⚪81,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30⚪?1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18⚪@1,2,3,4,5,6,7,8,9,10,11,12,13,14,15⚪A1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25⚪B1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45⚪C1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50⚪D1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28⚪E1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,39,31,32,33,34,35,36,37,38,39,40⚪ᓝ1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,39,31,32,33,34,35,36,37,38,39,40⚪---1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,39,31,32,33,34,35,36,37,38,39,40⚪ᓝ81,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,39,31,32,33,34,35,36,37,38,39,40⚪ᓝ?1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,39,31,32,33,34,35,36,37,38,39,40⚪ᓝ@1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50⚪ᓝA1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22

1⚪ᓝB1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35⚪ᓝC1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,3031,32,33,34,35,36,37,38,39,40,41,42,43⚪ᓝD1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23
ᦣᦪ⚪3⚪1.1.ᶍ1.2.ᶍ1.3.ᶍ1.4.ᶍ1.5.ᶍ1.6.ᶍ1.7.ᶍ1.8.ᶍ1.9.ᶍ1.10.ᶍ1.11.ᶍ1.12.HIᑡK⚪LMᓄOP/ᔜK૙஺஺ḄTU*(1)2+2=4VWXV3+3=6.(2)2+2=4Ḅᐙ⌕ᩩ\]3+3x6.(3)2+2^4_3+3=6`aᐙ⌕ᩩ\.ভc2+2*4,ᑣ3+3x6,efgᯠ.(l)p«->q,ᐸjp:2+2=4,q:3+3=6,TUa1.(2)p—rq,ᐸjp*2+2=4,q:3+3=6,TUa0.(3)”—q,ᐸjp:2+2=4,q:3+3=6,TUa0.(4)”—rq,ᐸjp:2+2=4,q:3+3=6,TUa1.1.13.HIᑡK⚪LMᓄOP/ᔜK⚪ḄTU*পclᜩ]n9ᑣoᜩ]n98.(2)pᨵlᜩ]n9oᜩr]n98.বlᜩ]n9VWXVoᜩ]n98.ভclᜩ]n9ᑣoᜩ]n9?.tP*lᜩ]n9;q*oᜩ]n98;r:oᜩ]n9?.পp#qQ1.ফq3p=1.বp—q=1.ভp~>i■■Vp=0xaT;p=lxaᎷ.1.14.HIᑡK⚪LMᓄ.(1)ᑢ᧽ᨴ}~~+.ফὁ]ᡈᓅ.বaᜩᡠᡃ.ভ_ᡂ.ম_]ᐘ.য_ᑢ¡¢£¤.

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18=(F(a)AF(b))AF(c))A(G(a)VG(b)VG(c))(2)VxVy(F(x)VG(y))QVxF(x)VVyG(y)=(F(a)AF(b)AF(c))V(G(a)AG(b)AG(c))বVxF(x)>VyG(y)=(F(a)AF(b)AF(c))-(G(a)AG(b)AG(c))ভVx(F(x,y)^3yG(y))«3xF(x,y)kmyG(y)=(F(a,y)VF(b,y)VF(c,y))->(G(a)VG(b)VG(c))5.3.à"#$D={1,2},ìĵôJ;ḄYÅII12,BC☢~ᙠII1R)⚪,gᙠ121RᎷ⚪.(1)Vx(F(x)-G(x))(2)3x(F(x)AG(x))(1)11:F(x):x<2,G(x):x<3F(1),F(2),Gপ,G(2)ᙳ),ᡠFVx(F(x)3G(x))0(õ1)>G(1)A(FফkG(2))).12:F(x);ll,G(x):x<0ᑣFপ,F(2)ᙳ),gGপ,G(2)ᙳᎷ,Vx(F(x)TG(x))Ꮇ.ফᶇÄíὅD÷ø.5.4.ᶍ5.5.ÄeYÅI᝞H(a)૙૙૙#$D={3,4}.(b)-f(x)-f(3)=4,-f(4)=3.(c)-F(x,y)-F(3,3)=-F(4,4)=0,-F(3,4)=-F(4,3)=l.UᦣᦪWX⚪Y24ùúᑡ~ᙠIḄ)*HপVx3yF(x,y)(2)3xVyF(x,y)(3)VxVy(F(x,y)kF(f(x),f(y)))(1)Vx3yF(x,y)=(õ3,3)VF(3,4))A(F(4,3)VF(4,4))=(0V1)A(1V0)=1(2)3xVyF(x,y)=(F(3,3)AF(3,4))V(F(4,3)AF(4,4))o(0A1)V(1A0)«0(3)VxVy(F(x,y)-F(f(x),f(y)))Q(F(3,3)kF(f(3))))A(F(4,3)>F(fভ,fব))A(F(3,4)>F(fব,fভ))A(F(4,4)kF(fভ,fভ))

190(0k0)A(1k1)A(1k1)A(0-0)ol5.6.ᶍ5.7.ᶍ5.8.ᙠ▤ᑡ⚪ᓄ⌕úᵨôJ;Ḅ*ý.(1)Iᨵ=þᦪḄÿᦪ.(2)Ḅ⚔.(1)F(x):xᦪ,G(x):xᦪ.ᔠᓄ3-x((F(x)AG(x))oVx(G(x)rG(x)).(2)F(x):xH(x,y):xyḄ,L(x,y):xy⚔.ᔠᓄ:-VxVy(F(x)AF(y)AH(x,y)->L(x,y))3x3y(F(x)AF(y)AH(x,y)A-L(x,y))=mx(F(x)A(3y(F(y)AH(x,y)AஹL(x,y)))5.9.ᶍ5.10.ᶍ5.11,ᶍ5.12.!"ᑡᔜ%Ḅ&'%.(1)VxF(x)VyG(x,y);(3)VxF(x,y)«->3xG(x,y);(5)3xlF(xl,x2))(F(xl)3-x2G(xl,x2)).&'%*+,Ḅ.(1)VxF(x)->VyG(x,y)Q3x(F(x)->VyG(x,y))-ᦣᦪ/0⚪225Q3xVy(F(x)G(x,y)).(3)VxF(x,y)O3xG(x,y)0(VxF(x,y)->3xG(x,y))A(3xG(x,y)->VxF(x,y))0(VxlF(xl,y)->3x2G(x2,y))A(3x3G(x3,y)Vx4F(x4,y))=3xl3x2(F(xl,y)G(x2,y))AVx3Vx4(G(x3y)->F(x4,y))z<=>3xl3x2Vx3Vx4((F(xl,y)->G(x2,y))A(G(x3,y)-»F(x4,y))).5.13.3"ᑡ4⚪5ᓄ⌕!5ᓄḄ7%ᐰ&'%(1)ᨵḄ:;<ᨵḄ=;>?@.(2)ᨵḄ=;૙૙஺ᡠᨵḄ:;>?@.বDᡠᨵḄ=;<ᡠᨵḄ:;>?@*Ḅ.(4)DᨵḄEF<ᨵḄ:;᠒*Ḅ.(1)F(x):x:;,G(y):y=;,H(x,y):x?@.3X(F(X)A3y(G(y)AH(x,y))«3xHy(F(x)AG(y)AH(x,y)).(2)F(x):x=;,G(y):y:;,H(x,y):x?@.3X(F(X)AVy(G(y)->H(x,y)))Q3xVy(F(x)A(G(y)H(x,y))).H┯JḄKᫀ:3xVy(F(x)AG(y)->H(x,y)).(3)F(x):x=;,G(y):y:;,H(x,y):x?@.Wx(F(x)Vy(G(y)H(x,y)))

20WxVy(F(x)->(G(y)->H(x,y)))<=>-VxVy(F(x)AG(y)H(x,y))(*&'%)«3x3y(F(x)AG(y)AH(x,y)).ভF(x):xEF,G(y)y:;,H(x,y):x?᠒.-3X(F(X)A3y(G(y)AH(x,y)))<=>-3x3y(F(x)AG(y)AH(x,y))(*&'%)=VxVyr(F(x)AG(y)AH(x,y))o@@@xVy(F(x)AG(y)•»f(x,y)).5.14.ᶍ5.15.ᙠQᯠSᳮUVFW᪀⌼"☢SᳮḄ[\(1)&]mxF(x)3Vy((F(y)VG(y))R(y)),3xF(x)^_:3xR(x).(2)&]:Vx(F(x)`(G(a)AR(x)))3xF(x)z^_:mx(F(x)AR(x))ব&]:Vx(F(x)VG(x)),TxG(x)^_:mxF(x)(4)&]:Vx(F(x)VG(x)),Vx(-G(x)V-R(x)),VxR(x)^_:VxF(x)-ᦣᦪ/0⚪226প[\জmxF(x)>Vy((F(y)VG(y))R(y))&]bᐭঝ^xF(x)&]bᐭঞVy((F(y)VG(y))R(y))জঝᎷgSᳮটPG)VG(c))R(c)ঞUIঠF(c)জEl@F(c)VG(c)ঠ▬jঢR6)টডᎷgSᳮণmxR(x)ঢEG(2)[\03xF{x}&]bᐭঝF(c)Efi)ঞVx(F(x)(G(a)A(R(x)))&]bᐭটF6)fGQ)AR(c))UI@ঠG(a)AR(c)ঝটᎷgSᳮডR6)ঠᓄmঢF(c)AR(c)ঝডᔠn@3x(F(x)AR(x))E@G(3)[\জFxG(x)&]bᐭঝVx-G(x)জoᣚঞf©UIঝ@Vx(F(x)VG(x)&]bᐭঠF஺VG(c)Ul@

21ডF(c)ঞঠ᪆nrs_ঢ3xF(x)EডG(4)[\®Vx(F(x)VG(x))&]bᐭঝF&)VG(y)UIজঞVxCG(x)V-R(x))&]bᐭট'஺"R(y)UIঞঠVxR(x)&]bᐭডRG)UঠঢP(y)টunrs_ণF&)ঝঢ᪆nrs_ডVxF(x)UG5.16.ᶍ-ᦣᦪ/0⚪2275.17.ᶍ5.18.ᶍ5.19.ᶍ5.20.ᶍ5.21.ᶍ5.22.ᶍ5.23.ᙠQᯠSᳮUVFW[\"☢Sᳮ(1)vᨵᳮᦪwᦪᨵḄᨵᳮᦪ᦮ᦪyzᨵḄwᦪ᦮ᦪ.(2)ᨵᳮᦪ{ᳮᦪwᦪ|ᦪ*wᦪyz|ᦪ}*ᨵᳮᦪ~*{ᳮᦪ.ব*ᙠ⊤ᡂᑖᦪḄ{ᳮᦪᨵᳮᦪ⊤ᡂᑖᦪyzᨵᳮᦪ*{ᳮᦪ.(1)F(x):xᨵᳮᦪ,R(x):xwᦪ,G(x):x᦮ᦪ.&]:Vx(F(x)->R(x)),3x(F(x)AG(x))^_:3(R(x)AG(x))[\03x(F(x)AG(x))&]bᐭঝF6)AG(c)জঞF(c)ঝᓄmটG(c)ঝᓄmঠVx(F(x)-»R(x))&]bᐭ@Ffc)-Rfc)U©ঢR(c)ঞডᎷgSᳮণR(c)AG(c)টঢᔠn@3x(R(x)AG(x))EGণফ:F(x):xᨵᳮᦪ,G(x):x{ᳮᦪ,R(x)wᦪ,H(x)|ᦪ&]:Vx((F(x)VG(x))R(x)),Vx(H(x)-R())x^_Vx(H(x)(*x)A-G(x)))

22[\জVx((F(x)VG(x)R(x))&]bᐭঝF&)VG(y))^R(y)UI@ঞVx(H(x)rR(x))&]bᐭটH&)fঞঠfreWG(y))ঝoᣚডH&)fG(y))টঠᎷgrs_ঢH&),(f‧rG(y))ডoᣚ-ᦣᦪ/0⚪228ণVx(H(x)(d(x)A-G(x)))UGঢব:F(x):x⊤ᡂᑖᦪ,G(x):x{ᳮᦪ,H(x)ᨵᳮᦪ&]:Vx(G(x)*x)),Vx(H(x)->F(x))^_:Vx(H(x)G(x))[\জVx(H(X)F(x))&]bᐭঝH&)-*Ffy)UXDঞVx(G(x)rF(x))&]bᐭটG&)--F(y)UIঞঠFG)-FSoডHG)-FG)rs_ঢVx(H(x)G(x))UG@5.24.ᙠQᯠSᳮUVFW᪀⌼"☢SᳮḄ[\vḄ*Q;.vᡈὅQ;ᡈὅ:;.ᨵḄ*:;ᡠᨵḄ*.(¡¢£¤ᔠ)F(x):x,G(x):xQ;,H(x):x:;.&]:Vx(F(x)->-G(x)),Vx(G(x)VH(y)),3x-H(x).^_3x-F(x).জVx(G(x)VH(y))&]bᐭঝG6VH(c)জUIঞ3x-H(x)&]bᐭটWfc)ঠG(c)ডVx(F(x)frG(x))&]bᐭঢF6)fffc)@UIণrFQ)তKF(x)ণEG5.25.ᶍ-ᦣᦪ/0⚪2290⚪¦6.1.⌱¨〉ªḄ«¬⊤"ᑡ¤ᔠপ5Ḅ᦮ᦪ

23ফ᜻᦮ᦪ¤ᔠ(3)10Ḅ᦮°ᦪḄ¤ᔠ(1){x|xG]A03}মS5={ீx,y>|x,ye]A0

24(3)0£{0}ভ0{e0}(5){a,b}c{,b,c,{a,b,c}}a-ᦣᦪ/0⚪230(6){a,b}{ea,b,c,{a,b}}{a,b}ga,b,{{a,b}}}(8){a,b}{£a,b,{{a,b}}}(1)ï(2)Ꮇবïভïমïযïï(8)Ꮇ6.6.ᶍ6.7.ᶍ6.8,ᶍ6.9,ᶍ6.10.ᶍ6.11.ᶍ6.12.ᶍ6.13.ᶍ6.14.ᶍ6.15.ᶍ6.16.ᶍ6.17.ᶍ6.18.ᶍ6.19.ᶍ6.20.ᶍ6.21.ᶍ6.22.ᶍ6.23.ᶍ6.24.ᶍ6.25.ᶍ6.26.ᶍ6.27.ᶍ6.28.ᶍ6.29.ᶍ6.30.ᶍ6.31.ᶍ6.32.ᶍ6.33.ᶍ6.34.ᶍ6.35.ᶍ6.36.ᶍ6.37.ᶍ6.38.ᶍ6.39.ᶍ6.40.ᶍ6.41.ᶍ

256.42.ᶍ6.43.ᶍ6.44.ᶍ6.45.ᶍ-ᦣᦪ/0⚪2310⚪ñ7.1.òóA={0,{0}},!AxP(A).AXP(A)={{0,0),<0,{0}),ீ0,{{0}}>,<0,{0,{0}}),ீ{0},0),<{0},{0}),{{0},{{0}}>,<{0},{0,{0}})}7.2.ô¤ᔠA,B,C,õAxBUAxC,ᔲ,íᨵBUCᡂöÜÚÛÜ*,íyᨵ÷ø:A=0,B={l},C={2},BUC,AxB=0=AxC.7.3.A,B,C,Dô¤ᔠ(1)![(AnB)XnD)=c)n6ù).(2)"ᑡ%WúᡂöÜûä*ᡂö?ᡂöḄýá[\*ᡂöḄþ,÷ø.(AUB)x(cUD)=(AxC)(UBxD)(A-B)x(C-D)=(AxC)-(B஺OD)পV(x,y)(x,y)(eAAB)x(cnD)=xeAOBAyWCCDo(xSAAxGB)A(ySCAySD)=(xWA/\yGC)A(xGBAyGD)<=>(x,y)(eAxB)A(x,y)(GCxD)<=>(x,y)eAxBACxD(AnB)XDD)=(A>C)ri®>D)(2)ᡂ,:A={1,2},B={2,3},C={1,2},D={2,3}(AUB)x(CUD)={1,23}X{1,2,3}=>(AXC)(UBxD);(A-B)x(C-D)={l}x{l}c(AxC)-(BxD)7.4.ᶍ7.5.A,Bᔠ!AxA=BxB,ᑣA=B.Vx,xeAQீX,Xு€AxAQீX,XுeBxB=xeBA=B7.6.ᑡ'(ᔠA={1,2}ᑮB={1}ḄᡠᨵḄ-ᐗᐵ0.R1=0,R2={(11)},R2={(21)},R3={(1,1),(2,1))./;7.7.ᑡ'ᔠA={2,3,4}1Ḅឤ3ᐵ0IA,ᐰ5ᐵ0EA,67ᡈ37ᐵ0LA,᦮◀ᐵ0DA.♦={{2,2},ீ3,3),ீ4,4)}EA=A;={(2,2),ீ2,3),<2,4),ீ3,2),ீ3,3),ீ3,4),(4,2),<4,3),ீ4,4)}LA=K2,2),ீ2,3),ீ2,4ு,ீ3,3),ீ3,4ு,ீ4,4)}DA={(2,2>,ீ2,4ு,ீ3,3ு,ீ4,4)}7.8.ᑡ'ᔠA={0,{0},{0,{0}},{0,{0},{0,{0}}}}1Ḅᒹ=ᐵ0.᧤={(0,0ு,ீ0,{0}ு,{0,{0,{0}}ு,ீ0,{0,{0},{0,{0}}}ு,({0},{0}),({0},{0,{0}}ு,ீ{0},{0,{0},{0,{0}>}>,ீ{0,{0}},{0,{0}}ு,ீ{0,{0}},{0,{0},{0,{0}}}ு,ீ{0,{0},{0,{0}}},{0,{0},{0,{0}}}ு}7.9.A={1,2,4,6),ᑡ'Aᑡᐵ0R:(1)R={ீx,y)|x,yeAAx+y#2}(2)R={(x,y)|x,yGAA|x-y|=l}

26BᦣᦪEF⚪H32বR={ீx,y)|x,yeAAx/yGA)(4)R={ீx,y)|x,yCA/\yJᦪ}(1)R={(l,2),ீl,4),,{2,D,ீ2,2),ீ2,4>,<2,6),ீ4,D,ீ4,2ு,<4,4),ீ4,6),<6,D,ீ6,2),ீ6,4>,<6,6)}=EA-{al)}(2)R={(1,2),(2,1)}(3)R={(1,1),(2,2),(4,4),(6,6),(24),(4,2),(4,1)}(4)R={(1,2),ீ2,2),ீ4,2ு,ீ6,2)}7.10.ᶍ7.11.RiLX1Ḅ-ᐗᐵ0M7xexNOᔠRi(x)=.|xRP.QᯠRi(x)£X.᝞TX={-4,-3,-2,-1,0,1,2,3,4},UVRl={(x,y)|x,yGXAx,ீ1,3ு,ீ2,4ு,<3,3),<4,2eAAB={{2,4)}domA={1,2,3}dom(AUB)={1,2,3,4}ranA={2,3/4}ranB={3,4,2}ran(APIB)={4}fld(A-B)={1,2,3}7.14.R={(0,1),(0,2),(0,3),(1,2),(1,3)X2,3)}WRDR,R-1,Rb{0,l},R[{l,2}].RDR={(O,2),ீO,3),ீ1,3)}R-1={{1,Oு,ீ2Qு,ீ3,O),ீ2Dீ3D(3,2)}

27Rb0,1}={(0,1),(0,2),(0,3),(1,2),(1,3)}R[{1,2}2,3}7.15.A={<0,{0,{0}}ு,ீ{0},0>}WAT,A2,A3,Ab{0},A[0],Ab0,Ab{{0}},A[{{0}}].A-1={ீ{0,{0}},0},{0,{0}>},A2={({0},{0,{0}})},A3=0,Ab{0}={{0,{0,{0}})},A[0]={0,{0}LBᦣᦪEF⚪H33Ab0=0,Ab{{0}}={({0},0)},A[{{0}}]=07.16.A={a,b,c,d},R1,R2A1Ḅᐵ0,ᐸjRl={{a,a>,},R2DRl={(c,d)},RI2={{a,a>,ீa,b),ீa,d)},R23={ீb,cு,ீb,dு,ீc,b)}7.17.A={a,b,c},l`'A1mnoḄᐵ0RIcR2,pqRI2=R1,R23=R2.Rl={(a,aு,ீb,bு},R2={(b,c),ீc,b)}7.18.Nᳮ7.4Ḅ(1),(2),(4).(1)FD0UH)=FDGUFDHsீx,y),(x,y)eFD(GuH)«3t«x,t)eFA(t,y)eGUH)«at(

28«3t((x,t)GFA(ty)GG)V3t«x,t)GFA(t,y)eH))/<=>(x,y)GFDGV(x,y)GFDH<=>,(x,y)(eGUH)DF=᳝(ீx,t)(eGUH)A(t,y)GF)«3t(((x,t)GGV(t,y)GH)A(t,y)eF))«3t({(x,t)GGA(t,y)eF)V«x,t)eHA(t,y)eF))=᳝(ீx,t)6Gvீt,yு6F)V3t«x,t)eHA(t,y)£F))=(x,y>6GDFVீx,y>6HDF=ீx,y)€GDFUHDF(4)(GCH)DFUGDFnHDFsீx,y),(x,y)(GGAH)DF«3t((x,t)(GGAH)A(t,y>eF)»3t(«x,t>eGAeH)A(t,y)eF))«3t(((x,t)GGA(t,y)GF)A«x,t)GHA(t,y)eF))=>at«x,t)eGA(t,y)eF)A3t«x,t)6HA(t,y)GF))<=>(x,y)GGDFUHDF7.19.Nᳮ7.5Ḅ(2),(3).(2)F|AUB]=F[A]UF[B]sy,BᦣᦪEF⚪H34yGF[AUB]<=>Bx«x,y>eFAXGAUB)«3x((x,y)eFA(xeAVxGB))<=»3x(«x,y)6FAxGA)V«x,y)eFAxGB))<=>3x«xy)GFAxGA)V9x«x,y)GFAxGB)/oyCRA]VyGF[B]«yGF[A]UF[B]ᡠtᨵF[AnB?F|A]UF[B].(3)Fb(AnB)cFbAAFbBs(x,y>(x,y)eFb(APB)0(x,y)6FAx(eAAB)oீx,yுCFA(xGAAxGB)««x,y)eFAxGA)A«x,y)eFAxeB)(x,y)GFbAA(x,y)eFbB=ீx,yுeFbACFbBᡠtᨵFb(AUB)UFbAAFbB.7.20.®RIcR2A1Ḅᐵ0,:

29(1)(R1UR2)-1=R1-1UR2-1(2)(R1AR2)-1=R1-1AR2-1(1)(R1UR2)-1=R1-1UR2-1sீx,y)(£R1UR2)-1<=>GRl-lA(x,y)ER2-1=ீx,y)£Rl-1AR2-1ᡠt(R1UR2)-1=R1

30-1AR2-17.21.ᶍ7.22.ᶍ7.23.ᶍ7.24.ᶍ7.25.ᶍ7.26.ᶍ7.27.ᶍ7.28.ᶍ7.29.ᶍ7.30.ᶍ7.31.ᶍ7.32.ᶍ7.33.ᶍ7.34.ᶍ7.35.ᶍ7.36.ᶍ7.37.ᶍ7.38.ᶍ7.39.ᶍ7.40.ᶍBᦣᦪEF⚪H357.41.ᶍ7.42.ᶍ7.43.ᶍ7.44.ᶍ7.45.ᶍ7.46.ᶍ7.47.ᶍ7.48.ᶍ7.49.ᶍ7.50.ᶍBᦣᦪEF⚪H36F⚪v8.1.1f:',U102XfXXX

31ᦪᦪ!᜻!ᏔWf(0),f({O}),f(l),f({l}),f({0,2,4,6,...}),f({4,6,8}),f({l,3,5,7})f(0)=0,f({0})={f(0)}={0},f(l)=l,f({l})={f(l)}={l},f({0,2,4,6,...})={f(0)f(2),f(4),f(6),...)={0,1,2,3,...}=,f({4,6,8})={f(4),f(6),f(8)}={2,3,4),f({l,3,5,7})={1,1,1,1}={1}.8.2.2.A={1,2},B={a,b,c},WBA.BA={fl,f2,f3,f4,f5,f6,f7,f8,f9}fl={(1,a),(2,a)},f2={(1,a),(2,b)},f3={(1,a),(2,c)J,f4={{1,b),(2,a)},f5={(1,b>,ீ2,b)},f6={(1,b),(2,c)},f7={(1,c),(2,a)},f8={(1,c),(2,bு},f9={(1,c),ீ2,c)}.8.3.3.`NyᦪfcᔠA,B᝞Azপf:R|R,f(x)=x,A={8},B={4}(2)f:R-^R+,f(x)=2x,A={1},B={1,2}(3)f:NfNxN,f(x)=(x,x+1},A={5},B={{2,3)}(4)f:N|N,f(x)=2x+l,A={2,3},B={1,3}(5)f:Z->N,f(x)=|x|,A={-l,2},B={1}(6)f:S3S,S=[0,1],f(x)=x/2+lA,A=(0,1),B=M,1/2]}f:S|R,S=[0,+8),f(x)=V(x+l),A={0,~},B={10(8)f:S-»R+,S=(0,1),f(x)=l/x,A=S,B={2,3}.Mt1fcA,B,ᑖtA⚪z(a)fLLᓫcḄ?᝞TfLḄWfḄyᦪ.(b)WAᙠfAḄf(A)cBᙠfAḄᐰf-1(B).844.ᑨAᑡyᦪjLḄLᓫḄLḄ?পf:'9',f(x)=x2+2(2)f:',f(x)=(x)mod3,x◀t3Ḅᦪ.বfz'>,10o

32XfxXᦪᦪ!᜻!Ꮤভf:'3஺1},001XfxXᦪᦪ!᜻!Ꮤ(5)f:'-{0}^R,f(x)=loglOx(6)f:R->R,f(x)=x2-2X-15BᦣᦪEF⚪H37পᓫVf(x)=x2+2ᙠ,1LᓫḄ.LVVxeIf(x)=x2+2*0.(3)LᓫḄ•ppf(0)=f(2)=஺LḄIVxe;001xfxXᦪᦪ!᜻

33!Ꮤ*2.মLᓫḄzf(x)=loglOxᙠ'1LᓫḄ.LḄVx£',f(x)=loglOxt2.8.5.X={a,b,c,d},Y={1,2,3},f={(a,1>,ீb,2),ீc,3)},ᑨtA⚪Ḅ૙૙Ꮇ(l)fL(XIJYḄ-ᐗᐵ0L(XYḄyᦪ(2)fL(XᑮYḄyᦪL(Lᓫ(3)fL(XᑮYḄL(ᓫভfL(XᑮYḄ.8.6.M7`NḄA,Bcf,ᑨfLᔲ(ABḄyᦪf:AB.᝞TL£fLᔲᓫḄ.পA=],B=',f(x)=x2+1.(2)A=',B=,,f(x)=l/x.(3)A=]x',B=_,f«x,y»=x/(y+l)..(4)A={1,2,3},B={p,q,r},f={(1,q),<2,q),<3,q)}.(5)A=B=',f(x)=2x.(6)A=B=\x\,f()=x2+2y2.(8)A=B=\,f(x)=1lx+.(9)A='x',B=',f«x,y,z))=x+y-z.8.7.7.A={a,b,c,d},B={0,1,2}প`'nyᦪfzAfB,pqfLᓫḄLḄ(2)`'nyᦪf:AfB,pqfLᓫḄLḄব¥¦`'nyᦪf:A|B,૙qfLᓫLḄᔩভ|A|=m,|B|=n,ᑖ£¨ᙠᓫyᦪf:A|BḄᩩª.পᫀ¬.f={(a,O),(b,0),(c,0),(d,0)}.(2)ᫀ¬.f={(a,0),(b,1),(c,2),(d,2)).(3)¥.®1AljB¨ᙠᓫz|A|=4>|B|=3.ভ¨ᙠᓫḄᩩªLm4n,¨ᙠḄᩩªLm>n,¨ᙠḄᩩªLm=n.8.8.`'¯ᯠᦪ'1Ḅyᦪf,pq(l)fLᓫḄLḄ(2)fLḄLᓫḄ.8.9.9.ALn7Cft(n>1),ᑣ(AᑮAḄyᦪjᨵ°±nyᦪᨵ°±nᓫyᦪ.(AᑮAḄyᦪjyᦪcᓫyᦪᨵn!n.²z®1(AᑮAḄyᦪjyᦪᨵn!n.8.10.10.f:'x',f((x,y))=x+y+1প£fLᔲᓫḄ(2)VA={ீx,y)|x,yG'Uf(ீx,y))=3},WAবVB={f(ீx,yு)|x,ye{l,2,3bl.x=y},WB.পfLᓫḄ“ீ0,1))="<0,஺)=2µLḄ,VVxe',f«x,y))>0.(¶fLḄ.

34(2)⌕pf(ீx,y))=x+y+1=3,¸s),f((3,3))}={3,5,7).8.11.ºNfLᔲ(XᑮYḄyᦪ»Mf:X|Yᢣ'LᓫLLḄ.পX=Y=\,\®ᦪஹ(x)=x2-x;(2)X=Y=\,f(x)=V-x;BᦣᦪEF⚪H38বX=Y=\,f(x)=1x(4)X=Y=]+={x|xe],x>0},f(x)=x+1;মX=Y=],f(x)=111XXXX8.12.f:STI(l)f(AAB)cf(A)Df(B),ᐸjA,Bcs.ফ¿'£3Àf(ACB)=f(A)nf(B)LÁÂÃḄ.ব£M7ÄÅyᦪ1Æ3ÀÃ.8.13.AÇÈᔠ,RA1Ḅ3Éᐵ0,g:A|A/R¯ᯠ᧜.পR᦮ᦪᔠ1ḄËnÌ3ᐵ0Wg(2).(2)£gḄឋÎ(ᓫ).(3)£ᙠÄÅᩩªA,gyᦪ.8.14.Sᔠ,A,BLSḄÏ,xT⊤ÑTḄᱯÓyᦪUxA={(a,1),(b,1),(c,0),(d,0)},XB={(a,0),A/R.8.17.17.f,g,h£RR,Uf&)=x+3,g&)=2x+l,h&)=1

352WfDg,gDf,fDf,gDg,hDf,gDh,fDh,gDhDf.8.18.18.f,g,he'ஹ,Uᨵf(h)=n+l,g(h)=2n,001xhxxᦪᦪ!Ꮤ!᜻WfDtgDf,fDg,hDg,gDh,hDgDf8.19.f:\T\,f(x)=x2-2,gz\■>\,g(x)=x+4,h:\h(x)=x-1.পWgDf,fDg;(2)gDfcfDgLᔲᓫḄ(3)f,g,hjyᦪᨵyᦪ᝞TᨵW'Ûyᦪ.8.20.20.f,gL('ᑮ'ḄyᦪU10,1,2,3()04,5XXfXXXXI>()23xXgxX

36ᦪᦪᏔ᜻পWfDg(2)£fDgLᔲᓫḄ.BᦣᦪEF⚪H39পÛÜḄÝᔠÞßLàÝᔠ:fDg(x):g(f(x)),áx=1,3,4tâᜧ75ḄᏔᦪä,f(x)LᏔᦪ;áx=0,2tâᜧ75Ḅ᜻ᦪä,f(x)L᜻ᦪᡠt1,11,1,322,30,40,400,250,255,52,2xxXXXXgxXXXXXX=((+==11=>=>IIIII3,ᦪ3ᦪᦪᦪᡈḄ᜻ᡈḄ᜻ᜧ7ḄᏔᜧ7ḄᏔ»UfDg:'|'.(2»LᓫḄ஺3=ὡ2)=3µLḄ:ç"={0,z1,2,3éê஻ìᜧ75ḄᏔᦪ}={0,1,2,3}U{3,4,

375,n,...}='.8.21.21.f:>'x',f(x)=ீx,x+1).প£fLᔲᓫcÄÅ(2)fḄyᦪLᔲ¨ᙠ᝞T¨ᙠW'fḄyᦪ(3)Wranf.পfLᓫḄVxl,x2G,,!xlrx2,íîjf(xl)=ீxl,xl+1)wf(x2)="2,x2+1).FLḄ,ï!ீ0,0)eranf,ᑣðG',pqf(x)=(x,x+1)=஺0)¶ÛL¸¥Ḅ.(2)ïf={ீx,ீx,x+l))|xG'}LᓫñḄ⌮ᐵ0f-1={((x,x+Dx>|Xd'}LyᦪL(ranfᑮdomf='Ḅyᦪ.fTL'x'>'Ḅyᦪïdomf-1=ranf*"x'.বranf={(n,n+11nG'}.8.22.f:]->],f(x)=(x)modn.ᙠ]1NO3Éᐵ0R,Vx,y£],x,y)€R=f(x)=f(y).পõßf(l).ফºNᖪ]/R.8.23.fl,f2,f3,f4®ᦪஹᑮ\Ḅyᦪ,Ufl(x)=1,01,0xxf2(x)=x,f3(x)=1,1,ᦪᑣ᦮ᔲ/f4(x)=1.ᙠ'1NO-ᐗᐵ0Ei,Vx,yG\,ீx,yு6Eiof(x)=f(y),ᑣEiL\1Ḅ3Éᐵ0ùfiú'Ḅ3Éᐵ0,Wᖪ\/Ei,i=1,2,3,4.8.24.24.M7tAᔠAcB,᪀⌼(AᑮBḄyᦪf:A|B.

38(1)A={l,2,3},B=Ub,c}(2)A=Q,1),B=Q2)(3)A=^|xGAx<0},B='(4)A=R,B=R+8.25.25.f:\x\T\x\,f(ீx,y))=((x+y)/2,(x-y)/2),fḄ.8.26.f:AfB,g:B^C,fDg:AfC.পf:A>BᓫḄ.(2)g:BCḄ.8.27.ᢥ᯿▤ᑮḄ!"᣸ᑡ%ᑡ&ᦪ(᝞*f(n)+g(n)Ḅ▤,-(ᑣ⊤01f(n)©(g(n)).x,V-n,logn,n3,nlogn,2n3+n,2n,(logn)2,Ign,n3+logn.8.28.(logn)logn=nloglogn.2ᦣᦪ45⚪7404logn=n2;2logn=n;2=n1/logn;2Iog2log2nnn=2ᦣᦪ45⚪7415⚪89.1.9A={a,b,c},B=2A,ᵫ:;P(A)=2A.9.2.2.0૙஺
1,2=
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0,1.9.3.3.A={2x|xG'},A='.9.4.4.:ᳮ9.1.9.5.5.:ᳮ9.3Ḅ(1),(3).9.6.A,B,C,DBᔠ,A=C,B=D,AxB=CxD.9.7.DEFGHIḄ,ḄJKB(LMNOP+,-Q.9.8.DEFGHIḄ'ḄJKBA,B,C,LM9.9.᪷TUᯠᦪḄBᔠ:;WX(1)36U,205

39(2)4-3,3®1(3)4U,m(4)1x4,22.9.10.ᶍ9.11.A,B1ZᦪB((l)AUBZᦪB.(2)AXBZᦪB.2ᦣᦪ45⚪7425⚪ᓝ10.1.ᑡE\%]XḄ]X⊤পA={1,2,12},VxCA,DxxḄ᎔ᦪ(ᓽDx=1X(2)A={l,234},Vx,y£AᨵxDy=max(x,y),max(x,y)x=yabcᜧḄᦪ.(1)11122122xxD(2)123411234222343333444444D10.2.ᶍ103ᶍ10.4.ᑨf%ᑡBᔠgᡠiḄjᐗ]Xᔲmn(1)᦮ᦪBᔠp=qrḄst]૙஺૙(2)uv᦮ᦪBᔠp*=qrḄ◀t]Xবᐰ{nxn>|▣BᔠMn(\)=|▣~tt]X(ᐸb2(4)ᐰ{nxn>Z⌮|▣Bᔠᐵ|▣~t=t]X(ᐸbn>2(5)>ᦪBᔠ'

40+=D]X(ᐸbD]X:;1Va,be\+,aDb=ab-a-bয+,n]={nz|zW]}.n]ᐵqrḄ~t=t]X.(7)A={al,a2,...,an},n22.D]X:;᝞%Vai,aj£AaiDaj=ai./(8)S={2x-l|xF]+}ᐵqrḄ~t=t]X.(9)S={O,1},SᐵqrḄ~t=t]X.(10)S={x|x=2n,nS]+},SᐵqrḄ~t=t]X.পmnফHmnব~t+tPmnভtmn(~tHmn(5)Hmnয~t+tPmn(7)mn2ᦣᦪ45⚪743~tHmn(tmn(9)~tHmn(tmn(10)~tHmn(tmn105g⚪bmnḄjᐗ]Xᑨfᔲ〉ᔠᣚ(ᔠ=ᑖ.পᨵᣚ(ᨵᔠব~t〉ᔠᣚ+ᔠt〉ᔠᔠtg~tᨵᑖ.ভt〉ᔠᔠ(6)~tᨵᣚ(ᔠtᨵᣚ(ᔠtg~tᨵᑖ.ᔠtᨵᣚ(ᔠ(9)tᨵᣚ(ᔠ(10)tᨵᣚ(ᔠ106g5⚪4bmnḄjᐗ]XDEḄᓫᐗ(vᐗ=ᡠᨵZ⌮ᐗḄ⌮ᐗ.পᨵᓫᐗ(vᐗ=Z⌮ᐗ.ব~tᓫᐗ1n▤ᐰ஺|▣(ᨵv(n▤|▣Mᨵ~t⌮ᐗ-Mtᓫᐗ1n▤ᓫ|▣(vᐗ1n▤ᐰ0|▣(Z⌮|▣M(ᑡH10)ᨵt⌮ᐗM-1.ভtᓫᐗ1n▤ᓫ|▣(ᨵvᐗ(¡Mᨵt⌮ᐗM-1.য~tᓫᐗ10,ᨵvᐗ(xḄ~t⌮ᐗ-xtvᐗ10,¢n=lᓫᐗ11,1=-1ᨵt⌮ᐗ(£U¤.ᨵᓫᐗ(vᐗ+Z⌮ᐗ

41ᓫᐗ11,ᨵvᐗ,1Ḅt⌮ᐗ1¥ᓫᐗ11,vᐗ0,1Ḅt⌮ᐗI(10)ᨵᓫᐗ(vᐗ+Z⌮ᐗ.10.7.ᶍ10.8.S=_x_,_1ᨵᳮᦪB,*1SḄjᐗ]X,Vீa,bு,ீx,y)6Sᨵீa,b>*ீx,y>=ீax,ay+b>(1)*]XᙠSᔲZᣚ(Zᔠ¨ᔲ1©-Ḅ¨(2)*]Xᔲᨵᓫᐗ(vᐗ¨᝞*ᨵ(ªᢣE(¬SbᡠᨵZ⌮ᐗḄ⌮ᐗ.পHZᣚ(Zᔠ(H®¯-.ফᓫᐗ1ᨵvᐗ(¢2°0,6,±Ḅ⌮ᐗ1ீ1ba->10.9.\1>ᦪB(:;\%²G&ᦪfl,...,f6.Vx,yG\ᨵflµx,yு)=x+y,f2«x,y))=x-y,f3((x,y))=x-y,f4(ீx,y))=max(x,y),f5((x,y))=min(x,y),f6(ீx,y))=|x-y|(1)ᢣE¶·&ᦪ'Ḅjᐗ]X.(2)gᡠᨵ'Ḅjᐗ]X¸ᔲ1Zᣚ(Zᔠ(ᗩ-Ḅ.বᡠᨵ'jᐗ]XḄᓫᐗ(vᐗ\஺஺஺º»GZ⌮ᐗḄ⌮ᐗ.2ᦣᦪ45⚪744পP\Ḅjᐗ]X(2)fl,f3,f4,f5,f6Zᣚ,fl,f3,f4,f5Zᔠ,f4,f5¯-(3)flḄᓫᐗ10,ᨵvᐗ,xḄ⌮ᐗ1-xf2ᨵᓫᐗ(vᐗ+Z⌮ᐗf3Ḅᓫᐗ11,vᐗ10,x(xwO)Ḅ⌮ᐗ11X;f4,f5,f6ᨵᓫᐗ(vᐗ+Z⌮ᐗ.10.10.½S={a,b},Sᨵ4Gjᐗ]X:*,D,i=“ᑖÀᵫ⊤10.8Á:.⊤10.8ababababaaaaababaaabbaabbabaabab*Di,পÂ4G]Xb¶·]X®ᣚ(ᔠ(Ã-ফºG]XḄᓫᐗ(vᐗᡠᨵZ⌮ᐗḄ⌮ᐗ.প*,D,•Zᣚ*,D஻Zᔠ(Ã-.(2)*ᨵᓫᐗ=Z⌮ᐗ,vᐗ1aDḄᓫᐗ1a,ᨵvᐗ(ºGᐗPUÆḄ⌮ᐗ•=(ᨵᓫ

42ᐗ(vᐗ=Z⌮ᐗ.10.11.S={1,2(…(10},Ë%☢:;Ḅ]XÍ஺஺஺+S᪀ᡂÐᦪÑÒீS,*)?᝞*Í᪀ᡂÐᦪÑÒᑣ¸*]Xᔲ®ᣚ(ᔠ(¬*]XḄᓫᐗ=vᐗ.(1)x*y=gcd(x,y),gcd(x,y)x+yḄᨬᜧÚÛᦪ.(2)x*y=lcm(x,y),lcm(x,y)x+yḄᨬÝÚÞᦪ.(3)**à=ᜧ-x=vḄᨬÝ᦮ᦪ.(4)x*y=âᦪpḄGᦪ,ᐸbx

43AA={fl,f2,f3,f4},ᐸfl={(0,0),(l,0)},f2={(0,0),(l,l)},⊤123411144212343132441414ffffffffffffffffffffffffD11.2.ᶍ11.3.ᶍ11.4.ᶍ11.5.ᶍ11.6.ᶍ11.7.G={a+bi|a,bS},iᦪᓫᓽi2=-1.Gᐵᦪ᪀ᡂ.ᦪᙠG#$%ᨵ'ᔠ(ᓫᐗO=O+Oi,a+biḄ⌮ᐗ-a-bi.11.8.ᶍ11.9.+᦮ᦪ-ᔠᙠ+#./0ᐗD᝞23Vx,y^,xDy=x+y-24+ᐵD5ᔲ᪀ᡂ7897᧕;<$%=>᦮ᦪx\z,&Dy)Dz=&+y-2)Dz=x+y-2+z-2=x+y+z-4xD(yDz)=x+(y+z-2)-2=x+y+z-4=x+y+z-4'ᔠ(ᡂ?.ᓫᐗ2.XḄ⌮ᐗ4-x.11.10.A={x|xG\@xxOA}.ᙠA#./CDᦪ᝞23fl6c)=x,12(x)=x-1,f3(x)=l-x,f4&)=(1-x)-1,ffi(x)=&-1)x-1,f6&)=x6-1)-1EFF6Dᦪ᪀ᡂḄ-ᔠ,DᦪḄᔠ.G)GHDḄ⊤.(2)(F,D
IJD.KᦣᦪMN⚪P47

44(1)123456112345622143653351624446251355361426645231ffffffffffffffffffffffffffffffffffffffffffffffffD(2)᧕;$%ឋRSᦪᔠᡂRS'ᔠ(ᓫᐗIfl,fl-l=fl,f2-I=f2,f3-1=f3,f4-I=f5,f5-I=f4f6z-l=f6.11.11.ᶍ11.12.ᶍ11.13.ᶍ11.14.G,TUᙠa௃G,WXG={ak|k£]}YGIZᣚ.z=>ai,aLaiaj=ai+j=aj+i=aja11.15.ᶍ11.16.G\VxGGᨵx2=eYGZᣚ.=>Gᐗ]a,b,ᵫa,b0▤ᐗ,a=a-1,b=b-1,`a

45ab=a-lb-l=(ba)-l=ba11.17.GYeGbJḄcdᐗ.acdᐗe9aa=aᵫfg(Xa=e.11.18.ᶍ11.19.*Y4▤ij2▤ᐗ.G4▤Gjᨵ4▤ᐗa,e9a2I2▤ᐗ3\Gkj4▤ᐗ᪷mnoᨽq.ᳮ,Gᐗ]Ḅ▤s5I2ᡈ1,aGkIuviᨵwᓫᐗUᙠF஺஺૙wᓫᐗyI2▤ᐗ.11.20.*GIwz{|YGUᙠᐗ]a}b,a~Tab=ba.ᐜGij3▤ᡈ3▤#Ḅᐗ].ᎷGsᨵ1▤ᡈ2▤ᐗe9G=ᐗ]aᨵa2=e.᪷m7⚪Ḅ',GAbel,.aGᐗ]T|a|>2,e9awaT,Eb=a-1,ᑣᨵab=ba.11.21.ᶍ11.22.ᶍ11.23.11.HIGḄ,XGG,ExHx-l={xhx-l|h£H),YxHx-1IGḄHḄᐳ.eIxHx-1Ḅᐗ]xHx-1w.=>xhx-l,xkx-lexHx-l,h,kGH,ᑣᨵ(xhx-l)(xkx-1)-l=(xhx-l)(xk-lx-l)=x(hk-l)x-1H,hk-1H,`ax(hk

46-l)x-1xHx-1.ᵫᑨ..ᳮ⚪X.11.24.ᶍ11.25.Y.ᳮ11.11.11.26.*10101010///01010101Gf=-KᦣᦪMN⚪P48পG#Ḅ0ᐗ▣GHGḄ⊤(2)HGḄᡠᨵবYGḄᡠᨵI.¡G▣¢£¤A,B,-B,-A.প⊤ABBAAABBABBAABBBAABAABBAফ:{A},{A,-A},{A,-B},{A,B},GবGIAbelᡠᨵḄIḄ.11.27.ᶍ11.28.ᶍ11.29,EG={],+}I᦮ᦪ.§ᖪ©,]/12]}4]/12].W>(4],4]+1,4]+2,4]+3}(4]+a)+@]+b)=4]+(12],12]+l,12]+2,12]+3,-;12]+ll)(12]+a)+(12]+b)=12]+(a+b)mod124]/12]={ফফ+4,12]+8}(12]+a)+(12]+b)=12]+G+b)mod1211.30,Á2ᔜÃ⚪G.ḄG1}G2Äf:Gl3G2,ÅYfIᔲG1ᑮG2ḄÇ᝱.᝞IÅYG

47IᔲᓫÇ᝱RÇ᝱}Ç᪀ɧÇ᝱Êf(Gl)}Ç᝱᪶kerf.পGl=(],+),G2=ீ\*,•),ᐸ\*wÓÔᦪḄ૙૙૙ᔠ,+}•ᑖÖ⊤×ᦪḄ}.f3]f\*,f(x)=11xXIᏔI᜻ᦪᦪ(2)Gl=(],+ᔣ2=3”ᐸ+}ᔵÖ⊤×ᦪḄ}Þ=ßH6@@ᑄ=1},ᐸÞᦪ-ᔠ.f:]-»A,f(x)=cosx+isiix(3)G1=(\,+)G2=(A,p),+}•ÄAḄ./Ç(2).f:\æA,f(x)=cosx+isinxপÇ᝱kIᓫÇ᝱~kIRÇ᝱.Ç᝱Ê{-1,1},Ç᝱᪶2].(2)Ç᝱,ᓫÇ᝱kIRÇ᝱Ç᝱Ê{cosx+isinx|xW]},Ç᝱᪶{0}.বÇ᝱RÇ᝱kIᓫÇ᝱Ç᝱ÊA,Ç᝱᪶{2kn|ke]}.11.31.ᶍ11.32.IG1êG2ḄÇ᪀Y-1IG2ᑮG1ḄÇ᪀.᧕;qp-1G2ᑮG1Ḅíîᦪ.=>G2Ḅᐗ]x,y,UᙠG1ᐗ]a,bWXqp(a)=x,qp(b)=y.ðᓃ,(P-l(xy)=qp-l(Cp(a)(p(b))=(p(Gl)Ḅᐗ]x,UᙠaidGl,WX

48FYô0a)5(G1)Ḅúᡂᐗ.11.35.G=(a)I15▤ö÷.(1)§HGḄᡠᨵḄúᡂᐗ.(2)§HGḄᡠᨵ.(1)úᡂᐗ:a,a2,a4,a7,a8,a11,a13,a14ফ:ব,ீa3)={e,a3,a6,a9,a12},{a5)={e,a5,a10},G11.36.஺)I5ᐗûᣚT1234512345/2145334512VA"পü-1,T-l,a-1TO(2)¡OTJ-1,0-1TO⊤ᡂkZḄýᣚþÿ.(3)
(2)Ḅᣚ⊤ᡂᣚ,᜻ᣚᏔᣚ.(1)1

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50orTOTO(3)()0()()00()()00()111412131412151315121413orTOTOOT᜻ᣚ-1,0-1TOᏔᣚ.1137.*!"#Gᐗ%a,b,c,&ab=acᔓᨵa-l(ab)=a-l(ac)ᓽ(a-la)b=(a-la)c,*+ᨵb=c.,ᳮ./!Ḅᡂ0.11.38.*1G2ᨵ▲,K2GḄ4,H2KḄ4[G:H5G:KKK:H].ᵫ78ᨽ:;ᳮᨵ|G|=[G:K]|K|,|K|=[K:H]|H|,<ᐭ>|G|=[G:K][K:H]|H|?᪷A78ᨽ:;ᳮᨵ|G|=[G:H]|H|,BCDEFGH⚪>.JᦣᦪMN⚪O50

51N⚪ᓝQ12.1.1A={a+bi|a,be],i2=-1},AᐵSTᦪḄUVWXV᪀ᡂZ[\]᦮ᦪZ.12.2.ᶍ123প1R1,R22ZR1aR2ḄbRlxR2c2Z,(2)&R1WR2dᣚZWefZR1XR2c2dᣚZWefZ.12.4.ᑨhiᑡkᔠWm;2ᔲ᪀ᡂZ᦮ZWo,᝞qrs᪀ᡂᳮᵫ.(l)A={a+bi|a,bd]},ᐸi2=-1,TᦪḄUVWXV.ফA={-1,O,1},vwUVWXV.বA=M2(]),2▤᦮ᦪz▣Ḅkᔠz▣UVWXV.(4)A2|}ᨵᳮᦪkᔠQ*vwUVWXV.12.5.ᶍ12.6.ᶍ12.7,ᶍ12.8.;ᳮ12.1(3)JᦣᦪMN⚪O51N⚪ᓝ~13.1.1.13.9m6EkḄ].ᑨhᐸ28.᝞qr28ᳮᵫ.(a),(c),প28.(b)Ḅ{e,d}ᨵᨬᜧi.(d)Ḅ{d,e}ᨵᨬᜧi.(e)Ḅ{a,b}ᨵᨬᜧi.13.22iᑡᔜkᔠS᦮◀ᐵ᪀ᡂkᑨhk28.(1)L={1,2,3,4,5)(2)L={1,2,3,6,12)(3)L={1,2,3,4,6,9,12,18,36}(4)L={1,2,22,...,2n},nG]+পr28ᐸ2.13.3.3.(1)஺12,&)Ḅ48.(2)3ᐗ[S3Ḅ48..dCbadba

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53L3Ḅ48:{a2},{b2},{c2},{d2},{a2,b2},{a2,c2}{a2,d2},{b2,c2},{b2,d2},{c2,d2},{a2b2,c2},zz{a2,b2,d2},{a2,c2,d2},{b2,c2,d2},L3b2dlc2a2LIb13.10acdaldlL2L3ভযফব]123⚪প((23))((123)X(12))((13))((D)S3(2)JᦣᦪMN⚪O5313.8.8.1ீL,YO28"#aGL.¢x|x6LAxYa}.(S,Y)2(L,Y)Ḅ48.S|£.Vx,yGS,ᨵxYa,yYa,*+xAyYxYa,xVyYaVa=aYa,S2xAySS,xVyGS,ᓽSA,V2¤¥Ḅ.¦§(S,Y)2ீL,Y)Ḅ48.13.9.9.┐13.9Ḅ¨E8᝞q8Ḅᐗ%©ᙠ⊡ᐗᑣ⊡ᐗ.(b),(d),(e)r28.(a)aad®⊡;b,cᨵ⊡ᐗ.(c)aaf®⊡;bḄ⊡ᐗc,d;cḄ⊡ᐗb,e;dḄ⊡૙஺஺b,e;eḄ⊡ᐗc,d.(f)aaf®⊡;bḄ⊡ᐗe;cWdᨵ⊡ᐗ;eḄ⊡ᐗb.13.10.10.13.9Ḅ¨E82ᔲᑖ±8ᨵ⊡8W²³8ᳮᵫ.(b),(d),(e)r28.(a)2ᑖ±8¦rᒹeaµ¶8W·¸8,᪀Ḅ48¹r2ᨵ⊡8W²³8b,cᨵ⊡ᐗ.(c)r2ᑖ±8r2²³8¦ᒹe·¸8º48¹2ᨵ⊡8aaf®⊡bWeḄ⊡ᐗᨵc,d;c,dḄ⊡

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55()()(()())()00()()()()()()()abcababcababcababcabcabcababcabcabcababcabcabcaacabcbacbbca''೙௜=AVA೙,,/=AVAAV,/,AVAA,,Z,////=AAVAAVAAAAz,,/z,=AAVAAVVAVA'''''''z=AAVAA^^^AAVAAVAAVAA'=A)()0()()0()00()bcabcabcabcabcbcacababc'''''AVAAVVAAVAAV'''''=AAVAAVAAVAA,ᳮᨵ()()()()()()abcbcabcacababcbc'a'''''©©=©©=AAVAAVAAVAA᧕ᔠ!ᡂ0.ᵫ0(0)(0)(l)0aaaaa''®=AVA=AV=ç஺ᓫÐᐗ.ᵫ()()000aaaaaa''®=AVA=V=,çaèéḄ⌮ᐗ.13.17.17.Ø.13.18.18.Ø.(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)15⚪JᦣᦪMN⚪O55N⚪ᓝêP2881,2,3,4,5,6,7,8,9,10,11,12,13,14,15,(Ø16,17),18,19,20,(Ø21-26),27,28,(Ø29~34),35,(Ø36~47),48,(Ø49-50)14.1.14.1m;i☢Ḅ(ëDEìᔣîDEᨵᔣ)Ḅkᔠ⊤½Ḅ஺ï⊤.G1=ீVI,E1ுᐸ,VI={vl,v2,v3,v4,v5},El={(vl,v2),(v2,v3),(v3,v4),(v3,v3),(v4,v5)};G2=ீV2,E2>,ᐸV2=VI,E2={(vl,v2),(v2,v3),(v3,v4),(v4,v5),(v5,vl)};Dl=(V3,E3>,ᐸV3=VI,E3={{vlv2),(v2,v3),(v3,v2>,(v4,v5>,ீv5,vl)};,D2=ீV4,E4)vᐸV4=VI,E4={(vl,v2ு,ீv2,v5),(v5,v2),ீv3,v4),

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ì-GḄ⊡/Ḅᦪ.|E(-G)|=|E(Kn)|-|E(G)|=n(n-l)/2-m.14.21.21,Sᔣ/G᝞/14.19ᡠ.পGḄᐰúᒘYhᒘY
ᢣᐸḄᒘh᫑(ᒘ)(2)GḄ56K(G)h56ᐭ(G).(1)ýIJYz{a,c},{d},dQᒘ.7ᒘY:{e5},{el,e3},{e2,e4},{el,e2},{e2,e3},{e3,e4},{el,e4},e5Q᫑.ফ¿+þᨵᒘ@ᨵ᫑
ᡠK=X=1.14.22.22.Sᔣ/G᝞/14.20஺஺஺
Ñÿ
⚔᪗.ᯠ
Ḅᐰᒘ᫑
Ḅ.14⚪
el
14.19e2e3e4e5acbdeᦣᦪ⚪!60᪗᝞
.3#ᒘ:d,f,h.3#᫑:e5,e9,el0.%&'ᨵᒘ)ᨵ᫑,ᡠK=X=1.14.23.23.
14.21ᡠ,
GḄK(G),ᐭ(G)6(G).K=2,X=3,8=4.14.24.24..G1/G2ᙳ&1ᔣ3ᓫ
,-G1/-G2ᑖ6&G1/-G2Ḅ⊡
.89Gl=G2:;<:-G1=-G2.14.25.25.=5▤3ᩩḄᡠᨵ@A᪀Ḅ1ᔣ3ᓫ
.ᡠ⌕=ḄD3ᓫ
ᵫFGᩩH᧕J⚔ᦪKLM

63123456,04Jdddddd{+++=f<

6414.26.26.=G5▤7ᩩḄᡠᨵ@A᪀Ḅ1ᔣ3ᓫ
.5▤7ᩩḄ1ᔣ3ᓫ
Ḅ⊡
D5▤3ᩩḄ1ᔣ3ᓫ
.ᑭᵨ25⚪=V4#LMᩩHḄ
{25⚪
~ᡠ,.14.27.27.6▤2-Nᑣ
ᨵ@A᪀Ḅᵫ13⚪ḄJ6▤2-Nᑣ
ᨵ@A᪀U&6Ḅᙌ#&3Ḅᙌ{n
ᡠ,.ᡈ14.28.28..n▤1ᔣ
&3-Nᑣ
;ᦪm/nLM2n-3=m,`᪵Ḅ1ᔣ
ᨵ@A᪀Ḅᵫᳮ,3n=2m,m2n-3=m,!Vn=6,m=9..GDLMᩩHḄ
ᑣ-GD6▤2-Nᑣ
YA᪀Ḅᨵ2#(27⚪)..Gl,G2ᙳ&1ᔣ3ᓫ
,G1=G2Q-G1=-G2.ᑭᵨ⚪]JLM⌕Ḅ1ᔣ
ᨵ@A᪀Ḅ{n
.14.29.29..GDn▤n+1ᩩḄ1ᔣ
89Gᙠ⚔vd(v)>3.,ᵨ8.GḄᨬᜧA£2,ᑣᢥᳮ2m42n,ᐸmDᦪ.cm4n,`/⚪.¡¢.14.30.30..e=(u,v)&1ᔣ
GḄzᩩ89:e&G᫑:;<:eYᙠGḄ£¤ᙌ.14.31.31..G/xḄ¥⊡
-GḄᦪᑖ6&mlm2,u¦GḄ▤ᦪ.14.32.32.u§V¨
ḄKᐭ.14.33.33..e=(u,v)&1ᔣ
G஺஺஺᫑89Uu(ᡈv)Dᒘ:;<:u(ᡈv)YD©ᢞ⚔.14.34.34.89Un(n22)▤3ᓫ
G«¬ᨵ#⚔YDᒘ.#6▤2-Nᑣ
#6▤2-Nᑣ
#6▤3-Nᑣ
25⚪
(a)(b)(c)(d)ᦣᦪ⚪!62uvD
Gᨵᨬᜧ®Ḅ#.)ᎷvDz#ᒘ.ᑣᨵz#w,x/uᙠG-vḄYAḄᑖ¯.cvᙠGḄ°zᩩὶuwḄ²³ᡠd(u,w)>d(u,v),`/uv´µ®ḄᨬᜧឋᎷ.¡¢.ᡠV,·¸ᙢu,YDᒘ.14.35.35..GDn▤1ᔣ3ᓫ
,n>3;&᜻ᦪ89G/-G᜻⚔Ḅ#ᦪ»¼.Vv£V(G)=V(-G)=V(Kn)d-G(v)+dG(v)=dKn(v)=n-1&Ꮤᦪ(n&᜻ᦪ)RDd-G(v)&᜻ᦪ¾ᨵdG(v)¿&᜻ᦪ.ᦑ-G/G᜻⚔#ᦪ»¼.14.36.36.1ᔣÁᐰ
Knᨵ@A᪀ḄᏔᙌᐸᑖ6&ᐸn14.37.37.n▤ᨵᔣÁᐰ
ᨵ@A᪀Ḅᙌᙌᐸᑖ6&ᐸn>2.

6514.38.38.n▤ÂÃ
«Äᨵ@A᪀Ḅᙌᐸn>3.14.39.39.1ᔣ
Gាᨵ#᜻⚔89`#᜻⚔¾ᯠ.14.40.40.(1)®u,v&1ᔣÁᐰ
KnḄ£Æ#YAḄ⚔d(u,v)&14.41.41..G.1ᔣ3ᓫ
,8(G)22,89GᙠᜧRᡈ¼R6(G)+lḄᙌ.14.42.42,.D=ீV,E)&z#ᨵᔣ
,;&3ᓫ
6(GR2,6-(G)20,8+(G)20,89DᙠᜧRᡈ¼Rmax{6-(G),6+(G)}+1Ḅᙌ.14.43.43.ᨵᔣ
D᝞
14.22ᡠ,.(1)DᨵĬ@A᪀ḄᙌᨵĬ@A᪀Ḅ3ᓫɲ(2)aᑮdḄËÌ~®d(a,d).(3)dᑮaḄËÌ~®d(d,a).ভᑨÏDDз
.(5)ÑDḄÒ
ÓÔ(1),(2),(3)Õ#⚪.14.44.44.ᨵᔣ
D᝞
14.23ᡠ,.(1)Dvlᑮv4&1,2,3,4Ḅ²ᔜ&ᩩ(2)Dvl«I]vl&1,2,3,4Ḅɲᔜ&ᩩ(3)D&4Ḅ²(Y×ɲ)ᨵĬᩩ&4Ḅɲ&Ĭᩩ(4)DQRᡈ¼R4Ḅ²&ĬᩩᐸᨵĬᩩ&ɲমᑏGDḄ]ÚÛ▣.ᑭᵨDḄÝÞÛ▣Ḅß4àá!⚪.ᦣᦪ⚪!632341200122000101010/100112100010100132225642121022211221443212102221inIlτIIuIlτIlτ

66AAAAপvlᑮv4&1,2,3,4Ḅ²ᦪᑖ6&0ᩩ,0ᩩ,2ᩩ,2ᩩãফvlᑮvl&1,2,3,4Ḅɲᦪᑖ6&1ᩩ,1ᩩ,3ᩩ,5ᩩã(3)D&4Ḅ²(Y×ɲ)ᐳ33ᩩ,&4Ḅɲᐳ11ᩩãভDQRᡈ¼R4Ḅ²ᐳ88ᩩᐸ22ᩩDɲãম%&DDæὶ
ᡠ૙஺஺]ÚÛ▣&4▤ᐰ1▣.14.45.45.ᨵᔣ
D᝞
14.24ᡠ,.:(1)v2ᑮV5&1,2,3,4Ḅ²ᦪ.(2)v5ᑮv5&1,2,3,4Ḅɲᦪ.(3)D&4Ḅ²ᦪ.(4)DQRᡈ¼R4Ḅɲᦪ.মᑏGDḄ]ÚÛ▣.14.46.46..D=(V,E)&4▤ᨵᔣ
,V={vl,v2,v3,v4},çJDḄÝÞÛ▣&0210001000010011A1JuDᔜ⚔Ḅᐭ/G.14.47.47.1ᔣ
G=(VE),V={vl,v2,v3,v4},E={el,e2,e3,e4,e5},ᐸᐵὶÛ▣&Z211100110000001100001MGnj

67uᙠA᪀Æén=GGḄ
ê.14.48.48.çJᙠÁᐰë
Kr,s,2W.পKr,s×ᨵĬ@A᪀Ḅᙌ(2)Kr,s«ÄᨵĬ#⚔§Y»ÝবKr,s«ÄᨵĬᩩ§Y»Ý(4)Kr,sḄK&í&!(1):î=1ïpðᨵᜧR¼R1Ḅᙌ.஺஺஺:2Wïᨵ&4,6…2rḄᙌxyòDᏔᙌ%@A᪀Ḅᙌᐳᨵr-1.(2)«Äᨵmax{r,s}#⚔§Y»Ý.(3)«Äᨵmin{r,s}ᩩ§Y»Ý.(4)K=ᐭ=minWs).ᦣᦪ⚪!6414.49.49..G.n▤mᩩḄ1ᔣ
89m2n-1.50..GD6▤1ᔣ3ᓫ
89GᡈxḄ⊡
-Gᙠ3#⚔§»Ý.ᦣᦪ⚪!65⚪ᓝôP303ᐰ1~22⚪15.1.ᑨÏ
15.11ÐaDõö
ÑYDõö
Ḅ«¬⌕÷Ĭᩩø^ᡂ&õö
(a),(c)òDõö
xyò;1᜻⚔.(b)YDõö
%&xY.(d)YDõö
,%&xY¿%&xᨵ᜻⚔.⌕ù(b),(d)ᡂ&õö
«¬⌕÷ᩩùxy;1᜻⚔.152ᑨÏnᑡ⚪Dᔲ&ûপÁᐰ
Kn(n23)òDõö
.ফn(n>2)▤ᨵᔣÁᐰ
òDõö૙஺૙.বÁᐰë
Kr,s(r,sᙳ&@0NᏔᦪ)òDõö
.প┯ýÁᐰ
Kn(n23)°#⚔ᦪòDn-1,⌕ùxᡂ&ᡂ&Ꮤᦪ⌕n&᜻ᦪ.ᡠÁᐰ
Knᙠn&᜻ᦪïøDõö
.(2)N¦.ᨵᔣÁᐰ
DæḄ;°#⚔Ḅᐭ¼RGᵫᳮ15.3J⚪&û.বN¦.Kr;s°#⚔ḄᦪYDrþDs,%òDᏔ⚔;Kr;sDḄ%Dõö
.15.3.3.=z#1ᔣõö
ùxᐹᨵ
পᏔᦪ⚔Ꮤᦪᩩ.ফ᜻ᦪ⚔᜻ᦪᩩ.বᏔᦪ⚔᜻ᦪᩩ.ভ᜻ᦪ⚔Ꮤᦪᩩ..(1)(2)(3)(4)3⚪(a)(b)(c)(d)15.11ᦣᦪ⚪6615.4.ᨵᔣ!ᐹᨵ

68(1)Ꮤᦪ⚔Ꮤᦪᩩ.(2)᜻ᦪ⚔᜻ᦪᩩ.(3)Ꮤᦪ⚔᜻ᦪᩩ.(4)᜻ᦪ⚔Ꮤᦪᩩ..15.5.5.ᙠk(kN2)$%ᜧ'ᡈ)'3Ḅᙌ(ᐰ஺஺஺/ᔣḄᡈᐰ0ᨵᔣḄ)2345675ᩩ8(ᨵᔣḄ6ᨵᔣ)9:ᡠ<0=4562kᩩ.>kᙌ0ClC2…,Ck,ᙠCi?@⚔A0vi,i=1,2,k.ᙠviBvi+1236CD,(vi,vi+1),(vi,vi+1),i=l,2…,kl.Aᡠ<Ḅ0G,ᑣGHIJᡠᨵ⚔Ḅ%ᦪK0ᏔᦪLMG0.456kᩩ.NkOPᑖḄHIHᡂHI45⌕6k-1ᩩ.>kᙌ0C1,C2.Ck,ᙠCi?@⚔A0vi,i=1,2,,k.ᙠviBvi+1236(vi,vi+1),i=l,2,...,k-1.T᪵6Vk-1ᩩWNkOPᑖḄᙌHᡂHIJviḄ%ᦪKXᡂ4(Ꮤᦪ),i=2,MvlBvkḄ%ᦪXᡂ3(᜻ᦪ)YᙠvkBvl236(vk,vl),!ZḄ%ᦪXᡂ4,ᐳ6Vkᩩ.Aᡠ<Ḅ0G,ᑣGHIJᡠᨵ⚔Ḅ%ᦪK0ᏔᦪLMG0.\]^⍝`65'k஺஺૙\:aᑮcḄ.15.6.6.de
fᨵᔣDgᑣDghHIḄ.L0D0LMiᙠjk>C0ᐸmḄᩩjk.n@vi,vjCV(D),ᑣvi,vjᙳᙠC±.'gvipavj,qJvjpavi,ᡠrDghHIḄ.15.7.7.>Ggាt2k(kN1)᜻%⚔Ḅ/ᔣHI.deGmiᙠkᩩ\uḄvᓫIkx1,x2,Tk,x1gᐸmᩩ.ᢥIkgvᓫIkJtmᡠᨵḄ.ᡠrx1gvᓫIkJE(n)=E(G),ᓽᡂ.Ꮇ>Gᨵ2k(kN1)᜻%⚔}⚪0.Gᨵ2(k+1)᜻%⚔}>u,vgGḄ᜻%⚔G=GU(u,v),ᑣG'ᨵ2k*21)᜻%⚔(u,vᙠG'mgᏔ%⚔)ᵫ{|Ꮇ>,G

69miᙠkᩩ\uḄপফবভ4⚪ᦣᦪ⚪67vᓫIk,x2,xk,Gg/ᔣHIde
fGmᨵ᫑ᡈᒘᑣG\g.(¤15.4)পdeᨵᒘḄ/ᔣHIG\g.>v0GmḄᒘᑣ{v}0Gmᒘ¥ᑣp(G-{v})>2>|{v}|=1ᵫᳮ15.6p^,G\g.(2)Ydᨵ᫑Ḅ\g.HIᨵ᫑Ḅᨬ§▤ᦪn=2,ᓽK2,MK2\g.y'▤ᦪn23Ḅᨵ᫑n᫑Ḅ©m45ᨵgᒘ.ᵫ(1)^T᪵Ḅª\g.d«fGgᑣGmᨵjk>0C.VvGV(C)=V(G),C-vgHIḄL¬G-vgHIḄ.L¬Gᨵᒘ.VeCE(C),feCE(C),®UG-eᨵHIḄ¯ᡂ°C,L¬gHIḄ.fedE(C),ᑣG-e±ᨵHIḄ¯ᡂ°C-e,LMgHIḄ.ᡠrGᨵ᫑.15.10.10deᳮ15.8.ᳮ15.8>u,v0n▤/ᔣvᓫGm\O²Ḅ⚔Jd(u)

70d(v)>n,ᑣG00GU(u,V)0((u,v)g6Ḅ8).(=):¶ᯠ.(<=)
>CgG,GU(u,V)mḄ••ᩩjk.পf8(U,v)\ᙠC\ᑣCgGmḄjk.ফf8(u,v)ᙠC?ᑣxC(u,v)gGmḄIk.জfu,vᙠGmO²ᑣxU(u,V)gGmḄjk.((u,V)\g8(U,V)).ঝfU,vᙠGm\O²,ᑣkd(u)>2(ᔲ®IJd(u)+d(v)<1(n

712)vir-1½vO²ᑣvlv2...vir-lvnvn-1…virvlgGmᩩjk.ᦣᦪ⚪6815.11.11.¿<Àᓽ\gª\g.456Áᩩ89:!ᡂ0?Ã456Äᩩ89:!Xᡂ=¿<Àg10▤3Åᑣ⌕ÆÇ◀ᡠᨵ᜻%⚔45⌕65ᩩ!XᡂÈ⚔Kg4%⚔ḄHIḄvᓫᡈÉvᓫ᝞(a)ᡈ(b)ᡠË.ÌÍ?¿<ÀgÎᨵIkᙠᐸmᩩIkḄ©236ᩩ8Ï<ᑮ᝞(c)ᡠË.15.12.12.de15.12m(a)\gÐgÎ.M(b)g.✌ᐜÓÔvᓫḄ⚪
fGᨵjkᑣGḄᡠᨵ2%⚔ᡠᐵὶḄ2ᩩ(×◀᜜)ØᙠGḄnᩩjk?.f(a)mg!ᨵ32%⚔ᐳᐵὶ6ᩩT6ᩩᙳᙠnÙjk?,'gᙠjk(ÚÛjk)?ÏÜÝÞ⚔v(mß'm3Ḅ⚔)!ᐵὶjk?Ḅ3ᩩ((a)mà⁐Ḅ3ᩩ)T¶ᯠ\p:.ᡠᨵ(a)m\g.âãäᑮ(b)mḄᩩjkåmàæçᡠË.ᡠr(b)mg.15.12(a)(b)11⚪(a)(b)(c)r=vl(u)v2...vn-lvn(v)vn=vvl=u1riv-rivᦣᦪ⚪6915.13.13.èᨵ2k(k22)éêᡂk⚗nì.í^Èéᙳ:½î᜜2k-1émḄkémḄnÙéïᡂ§ï(Èï2é)êᡂðZᐳñò៉ḄnìôT2ké:ᔲᑖᡂkï(Èï2é),Èïᡂ⚗ðZᐳñò៉Ḅnì=>V={vvgêᡂnìḄé},E={(u,V)U,vCV,UHVJU,V:ᔠ÷}<2k▤/ᔣvᓫG.ᵫí^ᩩø,Vu,vGV,

72dM)+dG)Nkᵫᳮ15.7Ḅùp^G0.'giᙠjk.>C=vilvi2"vi2kvil0ᐸmḄᩩjkᙠCmO²Ḅ⚔K:ᔠ÷.ᡠrprᑖᡂkï.15.14.14,èᨵnéí^ðZmḄnÙ«éᔠúᩭÔüᐸḄn-2é.de
n>3}Tné:᣸ᡂᑡ(n-2)+2=n.(2)'u,v,)*WJVweV-{u,v},w-$u.v)*.ᔲᑣ0᝞u.w,)*ᑣV,W,*2U,34u.wᔠ5ᩭ78$ᐸ:Ḅn-3$;<ᩩ>஺஺૙@.Ad(u)+d(v)22(n-2).n>3ITt,2(n-2)>n-l,ABCDপᡈফGHIᨵd(u)+d(v)2n-1,ᵫLᳮ15.7n,ᵫLᳮ15.7Ḅ^C<,Vu,veV,ᨵd(u)+d(v)>3+3=6=|V|.ᵫLᳮ15.7Ḅ^C<,G4OPQ,AᨵOPQ_S,|C=vilvi2"vi6vil஺஺૙ᐸNḄᩩ.}~⚔ᙠD12⚪(a)(b)ᦣᦪ⚪70CN)*r⚔⊤Ḅf⁐Ḅhstopᡂj⁐k.vil$vi2Ḅopvi3$vi4Ḅop,vi5$vi6Ḅopstiᡂ3Gj⁐kាᵨ6G,eḄf⁐.15.16.16.|ᐰKn(n23)Ḅ⚔ᑖyvl,v2,...,vn.KnNᨵ8mᩩ,eḄOPQ_S(y'ᙠ_SC1,C2N⚔Ḅ᣸ᑡWX,eyC1$C24,eḄ_S).᪀⌼KnNḄOPQ_S᝞⌱KnND1⚔(ᨵnG)D2⚔(ᨵn-1G),…,Dn-1⚔(ᨵ2G)Dn(ᨬ£)⚔(ᨵ1G⌱)¤¥D1⚔v

73¦§KnNḄᑮ)©Ḅ⚔ªᑮDn⚔ᯠ£¥Dn⚔§KnNḄ_ᑮD1⚔.᪵ᐳᑮn!ᩩKnNḄOPQ_S.᝞®,¯ᑖD1⚔ᡈ5(°4,¯ᑖDn⚔ᡈ±)²³Kn஺஺஺,eḄOPQ_Sᨵn!/n=(n-1)!ᩩ.15.17.17.|ᐰKn(n23)4´ᩗ(ᔜḄᩗᙳᜧ3ᡈ¹30).᝞~]vKnNᨬºḄOPQ_S»stᵨ¼½.¾¿´ᩗNOPQ_Sst,¯ᑖ_SḄ5(±)ÀᔣAKnNᐳᨵ(n-1)!/2ᩩ,eOPQ_S.ÁÂwᑡvᩭ¾¿ÂwḄᩗ¥NÃvᩗᨬÄḄᓽs.ᫀs,Ç.15.18.18.È☘ÊcËᙠÌÍA.ÎᜓᎷÑÒÓÔÕᑮÖB,C,D×ØÙᯠ£_ᑮÌÍA.15.13{vA,B,C,DḄÚÛÀÂwzÜḄÝ(Þ).ßàLÈ☘ÊḄØÙḄᨬºSá.4n=4Ḅâãä⚪.ᨵ(n-l)\fZ=3ᩩOPQ_S(,¯ᑖå/⌮┐ᔣ)ABCDA,ABDCA,ACDBA,ᩗᑖy32,46,44.ᐸNᨬºḄØÙSá4ABCDA,éê432Þ.15.19.19.K5ᐰ´ᩗ᝞15.14ᡠì]NḄᨬºOPQ_S.BAD1113761615.13Cᦣᦪ⚪૙஺஺71ᵨ¼½.¾¿´ᩗNOPQ_Sst,¯ᑖ_SḄ5(±)ÀᔣAKnN(Kn´ᩗ)ᐳᨵ(n-l)!/2ᩩ,eOPQ_S.n=5ᐳᨵ4!஻=12ᩩ.ᑡv12ᩩ,eḄOPQ_S,ᯠ£¾¿ÂwḄᩗÃvᨬºḄᓽs(ᨬºḄs,Ç).N(a),(b)îïáᡠì_S415.14NḄᨬºOPQ_SÂwḄᩗ432.15.20.20.|Gyn▤ᔣᓫᦪm=12(n-l)(n-2)+2,qrG4OPQ.ð½ñrm12(n-l)(n-2)+1,G,L4OPQ.

74✌ᐜqrGN}~,)*Ḅ⚔Ḅêᦪz.>n.ᵨôq.ᔲᑣõᙠu,v£V(G),öd(u)+d(v)12(n—l)(n—2)+2—(n—1),÷¾¿sm1N12(n-2)(r-3)+1.s4(n-2)▤ᔣᓫḄᦪᨬ8y12(n-2)(n-3)øù.34d(u)+d(v)2n.zᵫLᳮ15.7Ḅ^Cs<,GyOPQ.ᙠNn=5,m=7,Z[m>12(5-1)(5-2)+1=7,úÂ,4OPQ.12637884695abcde12637884695abcdeD19⚪(a)(b)1263

7578846915.145abcdeᦣᦪ⚪7215.21.21.|G=ீV,E)yᔣ.'ý3}þḄVIuV,öVIx0,ᙳᨵ-Vl)<|V1|,ᑣG4OPQ.tTÿᡂᔩᡂ.᝞K2ᩩ.ᩩ⌕ᩩᐙᑖᩩ.15.22.22,#Gn(n23)▤%ᔣ'ᓫᑣ*+,-./Ḅ⚔2vi,vj,ᙳᨵ+d(v)>n.567ᡂᔩᡂ.Ḅᩩᐙᑖᩩ⌕ᩩ.᝞5▤ᙌC5ᩩ.920⚪;<ᦣᦪ?@⚪A73@⚪ᓝCP319(E31-34)16.1.1.Gᡠᨵ5▤7▤IJ᪀Ḅ%ᔣ᪛.⚔2MᦪNWni=1di=2m=2(n1),1

76=@l+l+2+2+2+2+2=@l+l+l+2+2+2+3=ঞ1+1+1+1+2+3+3=@l+l+l+l+2+2+4=@l+l+l+l+l+3+4=@1+1+1+14-1+2+5=01+1+1+1+1+1+6.6ᑡo᦮ᦪ12Ḅ7fᑜᑖḄabf*eḼbfrsḄ7▤᪛ḄMᦪᑡ.r5ᐜuᶍ2M⚔2G7c"Jx"Ḅ᪛yᯠ{|}ᐭᡠuᶍḄ2M⚔212fJ᪀Ḅ7▤᪛;ᐸᙌᦪḄf᪛JxḄ.জঝঞ91⚪;<ᦣᦪ?@⚪A7416.2.2.bg%ᔣ᪛Tᨵ5ᱏ᪛U,3f2Mᑖ2ᐸḄᑖ23M⚔2Tᨵf⚔2ᑭᵨ᪛ḄឋᳮPm=n-1,m=2n-2=5x1+3x2+(n-8)x3.TḄ⚔2ᦪn=11.16.3.3.%ᔣ᪛Tᨵ8ᱏ᪛U,2f3Mᑖ2ᐸḄᑖ24M⚔2Tᨵf4Mᑖ2᪷TḄMᦪᑡsGgIJ᪀Ḅ%ᔣ᪛#Tᨵxf4M⚔2.ᵫᳮ᪛Ḅឋ8•1+2,3+Xe4=2(8+2+x—1)Ax=2.Mᦪᑡ(8.1,2.3,2.4).af᪛᪛Uᑤ◀{ᡠḄ᪛r5᪛Ḅ""(ᵨᓄ?Ḅ"")Ḅ⚔2᪛Ḅᑖ¡2.᪛TḄᑖ¡2ᨵ4f¢J᪀Ḅ4▤᪛ᨵ2f᝞£¤ᑖᐸḄ3M⚔24M⚔2Ḅ¥ᨵ6cJ᪀Ḅ¦§y᪛U⊡6ᩩḄ6fJ᪀Ḅ%ᔣ᪛;.ঠঞটডঢ©ঝ11g7▤%ᔣ᪛JxḄᨵ7c92⚪;<ᦣᦪ?@⚪஺஺૙7516.4.4.bg%ᔣ᪛Tᨵni(i=2,3…k)fiM⚔2ᐸ⚔2᪛UTe¬ᨵᱏ᪛U▤ᦪn=

772n+t,t᪛Uᦪ.ᑣm=2n+1-1.ᵫᳮ,201¯22kn=1+2t-2=2k=I+t.At2(2)k-W+2=3(2)-2+2.Q°16.5.5.n(n>3)▤%ᔣ᪛TḄᨬᜧMA(T)QR?ᨬ´?TḄᨬᜧMs1,ᔲᑣTḄ⚔2᪛U¢MᦪN=n32m=2(n-1).¢n▤¶·Pn᪛ᐸᨬᜧ

78M2.ᡠ5TḄᨬᜧMQR2.¸b¹☢»'ᓫTḄᨬᜧMs¼½n-1;¢n▤¾§Sn=Kl,n-1᪛ᐸMᦪn-1.ᡠ5TḄᨬᜧMᨬ´n-1.16.6.6.n(n>3)▤%ᔣ᪛TḄᨬᜧMA(T)=2,Tᨬ¿Ḅ¶·¿MÀA(T)=2,ᑣTḄMᦪᑡ1,1,2,2…2.Tᯠ¶·ᐸᨬ¿Ḅ¶·¿Mn-1.16.7.7.ÁÂPn(n஺2)▤%ᔣ᪛ÃÄ.»n(n22)▤%ᔣ᪛TQRᨵSᱏ᪛U¢᪛U᜻M⚔2.ᡠ5TÃÄ.16.8.8.ÁÂPn(n>2)▤%ᔣ᪛.IÆÇ᪛᪛Èᨵɶ»ÊÈᨵɶᡠ5.16.9.9.ÁÂ:,Ë%ᔣ᪛T¯Ì.6fIJ᪀᪛ᑖ¡2""4M3M93⚪;<ᦣᦪ?@⚪A76,Ë᪛ᙳ%ɶ»ÊÈᨵ᜻ɶᦑ¢¯Ì.16.10.10.᪵Ḅ᪛TÏÃÄÐÑᨵÆÇ᪛ÒÏÃÄÐ.16.11.11.ᙠᩩÔ%ᔣ᪛TÕÃÄIÆÇ᪛TQRᨵSᱏ᪛U⌕ᡂÕÃÄ,TÖាØSᱏ᪛U(᜻M⚔2).#TḄMᦪᑡ1,1,d2,d3,dn,ᑣdiW2(i=2,…,n).ᵫᳮ3k=±+2=2(n-l).3kÙ-2(n-2)=0,ᡈ3(2)n-2=0.di>2(i=2,n),+ᯠᨵdi=2(i=2…,n).»ÊTᯠ¶·Pn.¢¶·ÛÜÕÃÄ.;PÝÞßÝT¶·àTÕÃÄ.

7916.12.12.ᙠᩩÔ%ᔣ᪛TÕÀTÕᑣTᨵᶬá¶6Ønf⚔2(TᡠᨵḄ⚔2ᩩâ,ãᯠTᡠᨵḄâ(»Tᨵ(n-1)ᩩâ)ᡠᨵãᩩá¶äåæT.ᡠᨵÝÞßÝT¶·à,TÕ.16.13.13.Ô☢Sfo᦮ᦪᦪᑡçf(è)sᐙÝ%ᔣ᪛ḄMᦪᑡÀséG3gIJ᪀Ḅ%ᔣ᪛.(1)1,1,1,1,2,3,3,4(2)1,1,1,1,2,2,3,3(1)s.Ꮇ᝞ᨵã᪵Ḅ᪛ᑣ⚔2ᦪn=8,âᦪm=7.MᦪN=16*2-7,ëìᳮ.(2)sÔ.íP*9ফï⚪r5ᐜuᶍ2M⚔2Gðᡠ⌕GḄ᪛J᪀Ḅ᪛yᯠ{|⊡}ᐭ2M⚔2.16.14.14.#e%ᔣñáGḄbᩩâ,eᙠGḄ,Ëòᡂ᪛eeᨵឋeᐹᨵã૙஺஺Ḅឋ:eᙠGḄ,Ëòᡂ᪛=eGḄ᫑.(2)1,1,1,1,2,2,3,35fIJ᪀᪛.ᑖ¡2""3M2M8913⚪;<ᦣᦪ?@⚪A77(õö÷Áø)Ꮇ᝞e᫑ᑣG-eñáḄ»¢ᨵòᡂ᪛T.¢TGḄòᡂ᪛Øe.(u)(÷Áø)ÀGḄúgòᡂ᪛TØe,ûljG-eᨵòᡂ᪛T,»¢ὶáḄ¢ãðe᫑ýþ.16.15.15.#e%ᔣñáGḄbᩩâ,eᙠGḄ,Ëòᡂ᪛eeᨵឋ?eᐹᨵã᪵Ḅឋ:eᙠGḄ,Ëòᡂ᪛=eGḄÿ.(=)()GḄᨵᡂ᪛Tᐸ.Ꮇ᝞eᑣeᐵὶḄ⚔".#T$e,ᑣTUeាᨵᙌC,ᙌ'22($e.ᑤ*+ᙌ,-.e«e),/GḄᡂ᪛TUe-e01$e.(<=)()#GḄ-ᡂ᪛T$e,ᑣTᨵᙌ(3ᙌᙌ'41).16.16.16.e45ᔣ7GḄᩩ.,e:;᫑=>ᙠGḄᡂ᪛$e@4᪛AB>ᙠGḄᡂ᪛Ce4DᵫF14⚪HF15⚪IJKL/ᑮ.NᵫOe᫑ePᙠ-QᙌRSB4eᡠCeᡠᙠḄᙌḄ'Uᙳ>2.ᵨẚᙌ(ᓽᨵᙌZᑤ◀ᙌ,Ḅᩩ.)᪀⌼GḄᡂ᪛.জ3_ᑤ◀ᩩ.`aᑤ◀e.ᨬc/ᑮḄᡂ᪛$e.ঝᐜfeᑤ*ẚᣵeᡠᙠḄᙌᯠcẚᐸiḄᙌj᪵/ᑮḄᡂ᪛$e.16.17.17.T45ᔣ7GḄᡂ᪛-TTḄl᪛=-T$GḄᒘn(joᢣ.ᒘn).

804GḄ⚔"r᪛TstᡠCG-E(-T)Ḅ4-T$GḄᒘn.16.18.18.S45ᔣ7GḄᒘn(.ᒘn)=G[E(G)-S]$GḄᡂ᪛.4SGḄᒘnᡠCG[E(G)-S]Ḅ.GḄᡂ᪛ḄᡠCG[E(G)-S]$GḄᡂ᪛.16.19.19,ᙠ716.14ᡠ஺૙஺5ᔣ7.el,e2,e3a᪛AḄv᪀Ḅᡂ᪛ᐳᨵxyzR1{ᩭ.ᨵ(}~7).ele3716.14ᦣᦪ⚪7816.20.20.716.15ᡠ5ᔣ7ᨵxv᪀Ḅᡂ᪛yzRjQᡂ᪛ᩭ(0ᡠᨵ6▤v᪀᪛ᢧ⌱).6▤v᪀Ḅ5ᔣ᪛ᐳᨵ6Uᦪᑡᑖ4111115জ111124ঝ,111133ঞ,111223ট112222ঠC)=4,জḄᡂ᪛>ᙠḄ.ঝঞটঠḄᡂ᪛ᙳ>ᙠ.16.21.21.Kn(lᙠT᪀Ḅ7.GḄᔲᑣὃ⇋GḄ஺஺૙ᑖ¡.k@¢£.k=l`,TK2.46(G)21,ᡠCG¤ᨵᩩ..¥¦GḄᩩ.e,ᑣ{e}Ḅ§R7G[{e}](UG)T᪀.k=i■`(r21)`IJᡂK.©ª=«+1`¥¦TḄᱏ᪛®v,ᑣTl=T-{v}r+1▤᪛.ᵫ¢£Ꮇ,G>ᙠ7Gl=T1.ᙠTv¯ḄᑖA"4u,ᙠT1ᑮG1Ḅ᪀uḄG1Ḅ⚔"ele2e3F19⚪~7ele2e3716.15ঝঞটটঠᦣᦪ⚪79u'.ᵫOᙠG,dG(u')26(G)2r+0L,ᙠG1,dGl(u')4r,O>ᙠUᙠG°ᙠG1,±/(u',v')eE(G)./ᑮGḄ7GlU(u',v'),1T᪀.16.23.23.sn▤mᩩ.Ḅ5ᔣ7Gk(k22)᪛²ᡂḄ³᪍=:m=n-k.³᪍G$Ḅ᪛ᑖ4Tl,T2,...,Tk.ᵫ᪛Ḅឋ·mi=ni-1,i=1,2…k.

81O111(1)kkkiiiiiimmnnknk==-=-=-ૄ૙஺¹NGḄ3᪛,ᔜ¦⚔"Rᩩ'U4(k-1)Ḅº»«ᑣGU«Ḅ5ᙌ7(ᓽ᪛)$m+(k-1)=(n-1)ᩩ..Om=n-k.16.24.24,ᙠ716.16ᡠN7¼.ᡠḄᡂ7T+7Ḅᡂ᪛.পᢣRTḄD¾3ᩩDḄ¿ÀÁºHTḄ¿ÀÁºÂÃ.(2)ᢣRTḄᡠᨵ᪛A¾3ᩩ᪛AḄ¿ÀᒘnHTḄ¿ÀᒘnÂÃ.(a)70(l)c,d,g,h4D.1{Ḅ¿ÀÁº4Cc=cab,Cd=dabf,Cg=geabf,Ch=heab.¿ÀÁºÂÃ4{Cc,Cd,Cg,Ch).(2)a,b,e,f4᪛A.1{Ḅ¿Àᒘn4Sa={a,c,d,g,h},Sb={b,c,d,g,h},Se={e,g,h},Sf={f,d,g}.¿ÀᒘnÂÃ4{Sa,Sb,Ce,Cf}.(b)70(1)c,d,g,h,i4D.1{Ḅ¿ÀÁº4Cc=cbf,Cd=djaef;Cg=gfe,Ch=hjaeb,Ci=iaeb.¿ÀÁºÂÃ4{Cc,Cd,Cg,Ch,Ch}.(2)a,b,e,f,j4᪛A.1{Ḅ¿Àᒘn4Sa={a,d,h,i},Sb={b,c,h,i},Se={e,g,d,h,i},Sf={f,g,d,c},Sj=[j,h,d}.¿ÀᒘnÂÃ4{Sa,Sb,Ce,Cf,Cj).16.25.25.zR716.17ᡠÄᩗ7ḄᨬÆᡂ᪛.abcdegfhijabd

82egh(a)(b)ᦣᦪ⚪80ᵨKruskalÇ/7ᑖḄᨬÆᡂ᪛}È7¼ÉÊᡠ.(a)7W(T)=27,(b)7,W(T)=14.16.26.26.T4vËÌ᪛,(T)2k,=T¤ᨵkᱏ᪛®.Tᨵxᱏ᪛®ᑣTᨵn-xᑖA"(Uᦪ>2),ᐸ¤ᨵ1⚔"Uᦪ4A(2k).ᵫ᪛Ḅឋ·¾ÍÎÏᳮ2m=2(n-1)=Jd(v)>x-1+(n-x-1)-2+A.᦮ᳮ/x>>k.NÒvev(T),±d(v)=A(T)>kᑣT-vᨵAᑖ¡(ᙳ4᪛).#᪛4ËÌz᪛ᐸÓ⚔"TḄ᪛®Ô#᪛ËÌ᪛ᑣ¤ᨵ2ᱏ᪛®ᐸ¤ᨵ1ᱏªv¯)TḄ᪛®.ᡠCT¤ᨵÕk)ᱏ᪛®.16.27.27.C45ᔣ7GḄᙌ,el,e2WE(C),=G>ᙠ$.el,e2Ḅᒘn.ᎷG7ᔲᑣὃ⇋$ᙌCḄᑖ¡.ᵫឋ,Gᨵᡂ᪛.Ò«=C-el,G0=G-el,ᑣ«G0ᩩº».#G0ᨵᙌᙌ,Pᨵ.ᙠ«,G0ᑤ◀+./G1;#G1Öᨵᙌ×ᑤ◀-ᙌ,ᙠ«,Ḅᩩ./G2;ØÙjrÚÛ¤/ᑮ$ᙌḄGk,1GḄᡂ᪛$«($e2),°$el.Gᡂ᪛GkḄᵫ᪛Ae2ᡂḄ¿ÀᒘnSe2Pᯠ$el,ᔲᑣe2ᐵὶḄ⚔"ᙠG-Se2Ü«-e2Uel=C-e2Öᯠ.1258111498109521415453423(a)(b)716.1755

831258111498109521415453423(a)(b)F25⚪~7ele2rᦣᦪ⚪81(a)16.28.28.Tl,T25ᔣ᪛TḄ7Ý(a᪛BsE(T1)ClE(T2)W0,=§R7G[E(T1)nE(T2)]᪛.T3=G[E(T1)ClE(T2)].4T3TḄ7ᡠCT35Áº.Vu,vGV(T3),4u,vaT1Ḅ⚔"ᡠCᙠT1ᨵuᑮvḄº»«1;ÞßᙢᙠT2ᨵuᑮvḄº»«2.«1,«2a᪛TḄº»ᙠ᪛I⚔"Ḅº»áᨵᩩᡠC«1=«2.O«1=«2ᙠT3jâ=u,vᙠT3Ḅ.ᡠCT3Ḅ.ᡠCT3=G[E(T1)AE(T2)]᪛.16.29.29.G4n(n25)▤ãᓫ7=Gᡈ-GP$ᙌ.✌ᐜᑭᵨF23⚪ḄIJèé5ᙌḄ7(³᪍)Ḅ.ᦪm=n-psn-l.()Ꮇ᝞GH-Ga$ᙌᑣ12(1)()()()2(1),nnnEKEGEGn-==+<ᱛn(n-4)<0,j(n>5)ëì.16.30.30.Tl,T25ᔣ7GḄᡂ᪛selT1Ḅ᪛ABT2ḄD,=0>ᙠ.e2T1ḄDBT2Ḅ᪛A±/(Tl-el)U{e2}H(T2-e2)U{elíGḄᡂ᪛.ᵫOel஺OOT1Ḅ᪛A,T2ḄDᡠCel(ᙠ¥îᡂ᪛ᓃ;᫑(᫑ᙠ¥îᡂ᪛,).

84ὃ⇋GḄT1ḄᵫelᡂḄ¿ÀᒘnSTl(el),HGḄT2ḄᵫelᡂḄ¿ÀÁºCT2(el).STl(el)P$CT2(el)Ḅ¤ᩩ.ᓽSTl(el)ACT2fcl)N0;ᔲᑣelḄð"u,vᙠG-STl(el)ᨵºSTl(el)GḄᒘnñ.STl(el)nCT2©1)¥¦ᩩ.ᑣe2T2Ḅ᪛A,T1ḄD.(Tl-el)U{e2}Ḅ(5Áº(GḄᡂ7òGḄᡂ᪛.(T2-e2)U{el}Ḅ(5Áº(GḄᡂ7ò1;GḄᡂ᪛.16.31.ᶍ16.32,ᶍ16.33.ᶍ16.34.ᶍ16.35.35.zRᡠᨵv᪀Ḅn(l

85(a)(b)(c),2⚪-RIRORORO(a)(b)(c)17.15(a)(b)(c),1⚪-.ᦣᦪ01⚪284(b)Wdeg(Ri)=18=2m(m=9).(c)Zdeg(Ri)=18=2m(m=9).17.3.3.17.16ᡠ3஺஺૙☢ᐭᐜ5ᔜ)᪗789ᯠ;ᔜ☢Ḅ)<&#ᦪ.(a)R0Ḅ)<ele2e5e6e8e7,deg(RO)=6.R1Ḅ)<ele2e3,deg(Rl)=3.R2Ḅ)<e4e5e6,deg(R2)=3.R3Ḅ)<e3e4e8e7,deg(R3)=4.(b)ROḄ)<ele2e3e4e5e5e4e8e7,=ᩖ?@deg(RO)=9.R1Ḅ)<e2(A),deg(Rl)=1.R2Ḅ)<ele6e7,deg(R2)=3.R3Ḅ)<e3e8e6,deg(R3)=3.(c)R0Ḅ)<ele2e3e3e2De4e8e8e7e6e5Eᡂ,deg(RO)=11.☢RORIR2R3R4R5*#ᦪ33333318☢RORIR2R3R4£#ᦪ4343418(a)(b)(c)17.16(a)(b)(c),3⚪-RIR3R2e7R2R3RI

86RIR2ROele2e3e8ROe4e6e5ROele2e3e4e5e6e7e8ele2e3e4e5e6e7e8.ᦣᦪ01⚪285RIḄ)<el,deg(Rl)=1.R2Ḅ)<e4e7e6e5,deg(R2)=4.17.4.4,ᙠ17.16ᡠḄ(a)HIJ☢ᐭK᜜M☢Ḅ#ᦪᑖ3&4.,(2),(3)17.16(a)Ḅ☢ᐭᐸফḄ᜜M☢Ḅ#ᦪ3,(b)Ḅ᜜M☢Ḅ#ᦪ4.17.5.5.17.17ᡠ☢Ḅ☢Ḅ)<&#ᦪ.2PQᨵ᜜M☢ᐸ)<=ᩖ?@abcefegecdcba,#ᦪ12.17.6.6."7ᳮ17.6:TGn(n23)▤᩽ᜧ☢ᑣGYZᙠᒘ\&᫑.প"G_ᒘ\.(a"b)Ꮇ᝞Gᨵᒘ\vO,ᑣG'=G-v☢efgᨵ*hiᑖj.ᙠGDvOklḄ⚔\nᨵ*⚔\(ou,v)ᑖpG'ḄYqhiᑖj.G'U(u,v),rsGU(u,v)t☢uDG᩽ᜧ☢vw.(2)"G_᫑.(a"b)Ꮇ᝞Gᨵ᫑e=(u,V).ᵫ(Gy᩽ᜧ☢hiḄzGfgᨵ3⚔\ᡠuDvfgᨵ⚔\{ᦪ>2.Y|Td(u)>2,ᑣuGḄᒘ\}ᵫ(1)~GYᨵᒘ\.17.7.7."17.18ᡠM᩽ᜧ☢.

87প,4⚪-বফ17.17abcdg.ᦣᦪ01⚪286(a)Ḅᨵ☢ᐭG1,(b)Ḅᨵ☢ᐭG2()
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8817.21.ᦣᦪ01⚪288K3,3ᨵn=6⚔\,m=9ᩩ)m=8V3n-6=3-6-6=12.}K3,3Y☢.ᡠ7ᳮ17.125ḄY¦ᓫ☢Ḅᐙᑖᩩ©.17.14.14.TG¦ᓫ☢☢ᦪr<12,6(G)23."GZᙠ#ᦪ(ᡈ'(4Ḅ☢.«¬r=12®¯°±Y².Y|TGhiḄᔲᑣὃ⇋
Ḅhiᑖj.ᵫGḄhiឋ·n-m+r=2;ᵫ6(G)23·¸¹7ᳮ2m>3n;ᵫ7ᳮ17.4.2m=£deg(Ri).ᵫ¯☢^deg(Ri)<6r-12.º»ᑮr<12,~☢Ḅᙳ#ᦪIdeg(Ri)/r<6-l?/r<5.s☢Ḅ#ᦪ᦮ᦪᡠZᙠ#ᦪ(ᡈ'(4Ḅ☢.17.15.15.TGn▤mᩩ)Ḅ¦ᓫ☢~m<30,"6(G)44.ᵨa"b.ᔲᑣᎷTVvGV(G),d(v)25.ᵫ¸¹7ᳮ¿~2m>5nᵫ7ᳮ17.12¿~m<3n-6ᵫ¯*Y'ÀÁn,ᑮm230,uDm<30kvwᡠ6(G)S4.17.16.16.TGn(n211)▤_ᔣ¦ᓫ"Gᡈ-Gn☢.(a"b)Ꮇ᝞Gᡈ-G☢
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ḄᏔtq᪀ᔩ17.23(a)(b)(c),20⚪-(a)(b)(c),19⚪-13Yq᪀Ḅ6▤hiḄ¦ᓫḄ☢.ᦣᦪ01⚪291Yq᪀Ü⚪-.17.22.22."7ᳮ17.18.7ᳮ17.18TG*ᐹᨵk(k22)hiᑖjḄ☢GḄᏔ,n*,m*,r*&n,m,rᑖG*&GḄ⚔\ᦪ)ᦪ☢ᦪᑣপn*=r;(2)m*=m;(3)r*=n-k+1;ভTG*Ḅ⚔\vi*à(GḄ☢Ri,ᑣdG*(vi*)=deg(Ri).ᵫG*Ḅ᪀⌼~,প(2)âᯠḄ.ভ"ãä7ᳮ17.17Ḅ"(,2004.p332).uå"(3).æᵨ·ᐸ¡ç.ᵫ(è☢ḄᏔhiḄsᵫn*-m*+r*=2.

90éᵫḄ¡çᨵn-m+r=k+l.(*=2+m*-n*=2+m-r=n-k+l.17.23.23.!"êW6,W7ëᏔ.-.17.24(a)(b),21⚪-(a)(b).ᦣᦪ01⚪29217.24.24.Tn▤mᩩ)Ḅ☢ëᏔ"m=2n-2.TG*GḄᏔGëᏔᡠG*SGᵫ(ᏔhiḄ☢sGhiᡠᓽn-m+r=2ᐸrGḄ☢ᦪ.en*=n,ᵫ7ᳮ17.17¿~,r=n*=n,íᐭn-m+n=22m=2n-2.17.25.25.TGn(n24)▤᩽ᜧ☢"GḄᏔG*2)-hiḄ3-ïᑣ."ᢥ᩽ᜧ☢Ḅ7ñ,G¦ᓫ.G_AᡠG*_᫑s2-)hiḄ.ᵫ7ᳮ17.7~GḄ☢Ḅ#ᦪᙳ3,òᵫ7ᳮ17.17~G*⚔\Ḅ{ᦪᙳ3.ᵫ7ᳮ17.6~Góᨵ᫑òG*_A.zᵫ(n>4,ᡠGḄ*☢Ḅ)<¯fôᨵᩩᐳ)òG*_).(G¦ᓫe3-ïᑣḄ.17.26.26."☢GḄᏔG*eöG☢Ḅ#ᦪᙳᏔᦪ.n⌕ឋ.ᵫ(G*sVvGV(G*),dG*(v)Ꮤᦪ.sdG*(v)'(vᡠᙠGḄ☢RḄ#ᦪ,ᓽdG*(v)=deg(R).(,deg(R)Ꮤᦪ.zGḄè☢ᑁᙳᨵG

91*Ḅ⚔\ᡠGḄ☢Ḅ#ᦪᏔᦪ.ᐙᑖឋ.ᵫ(ᏔhisᨵG*hi.zVvev(G*),nZᙠGḄ☢R,KᐸvᙠR.(dG*(v)=deg(R)ᏔᦪsG*.17.27.27.TG*☢GḄᏔ,G**G*ḄᏔᙠøù,GDG**7Yq᪀G**☢G*ḄᏔsúhiḄ.GYhi®7DG**Yq᪀.17.28.28.5ᑡᔜḄ⚔\ᵨü¿gḄý⁐Ḽ⁐.প5▤N5.(2)5▤ᙌC5.23⚪(a)W6WW6*(b)W7MW7*ᦣᦪ⚪93(3)6▤ᙌC6.ভ6▤ᐰK6.(5)6▤W6.য7▤W7.(7)ᐰK3,4..17.29.29.17.25ᡠᔜḄ⁐ᦪ.K3,ᡠ!⁐ᦪX23."#ᵨ3%&⁐'⚔Ḽ⁐*᝞,(a)ᡠ*ᡠ!X<3,./x=3.(b)K5,ᡠ!⁐ᦪX25."#ᵨ5%&⁐'⚔Ḽ⁐*᝞,(b)ᡠ*ᡠ!XV5,./X=5.ব12342*ᦑ⁐ᦪX=2.(a)(b)(c)17.25N5x=1C5X=3C6X=2K6

92X=6W6X=4W7X=3W3,4X=228⚪ᦣᦪ⚪9417.30.30.6T2789᪛*;⚪ᓝ@9⚪AB*789ḄCᔣ᪛E2(.G᪛4ᙌ*H4᜻ᙌ)*3KLMᩩO*ᡠ!⁐ᦪ22.17.31.31.6G2n▤k-Pᑣ*;tuᎷ6,G-v26-jḼ⁐Ḅ.RbG-vḄMT6Ḽ⁐*UvXḄᡠᨵ5T⚔ᨬ[ᵨ5%&⁐*ᦑj!ᵨ6%&⁐ᒕ,ḄM%'⚔vḼ⁐*᪵GḄMT6Ḽ⁐.17.33.33.ᵨLḄ&⁐'17.26ᡠḄᙢ☢Ḽ⁐.(a)ᙢḄRᏔ23-()jḼ⁐Ḅ*.GK3,ᡠ!⁐ᦪ>3.'ḄᙢKL⌕3%&⁐sk☢Ḽ⁐.(b)ᙢRḄ8☢2Ꮤ▤W6,ᐸRᏔ2W6(RᏔ)*⁐ᦪ24(ᳮ17.21).'1ᙢḄ☢Ḽ⁐KL⌕3%&⁐.(a)(b)(c)29⚪©ব17.26ᦣᦪ⚪95(c)ᙢ2᜻▤W7„2RᏔ*⁐ᦪ23.KL◤⌕3%&⁐'1ᙢḄ☢

93⁐.ᔜᙢḄᨬLḼ⁐,ᔜRᏔḄ⚔Ḽ⁐ᡠ.17.34.34.17.26ᡠᔜᙢḄRᏔḄ⁐ᦪ*ᔜᙢḄ☢⁐ᦪ.ᙠ33⚪(a)ᙢḄ☢⁐ᦪx*=3;(b)ᙢḄ☢⁐ᦪx*=4;(c)ᙢḄ☢⁐ᦪx*=3.17.35.35.W2kUW2k+1ᡠRḄᙢḄ☢⁐ᦪ.Wn2RᏔ*ᐸRḄᙢḄRᏔ2Wn,ᓽWn*=Wn.ᡠ!x*(Wn)=x(Wn*)=X(Wn).ᦑx*(W2k)=X(W2k)=4,/x*(W2k+l)=x(W2k+l)=3.17.36.36.6G*G17.27ᡠ8☢GḄRᏔ.£G*.x(G*)GRᙢḄx*(G).G*᝞,¤¥ᡠ*2,X(G*)=2./x*(G)=X(G*)=2.17.37.37.'ᐰK4¦K5ḄOḼ⁐.,.X*(K4)=4-1=3.x'(K5)=5.(b)(c)(a)33⚪36⚪17.27ᦣᦪ⚪9617.38.38.'K3,3ḄOḼ⁐.,.X'(K3,3)=A=3.17.39.39.;<§¨ḄO⁐ᦪx'=4.§¨Ḅᨬᜧ|A=3,ᵫ«¬ᳮ34XY4.,☢;<3%&⁐4#'OḼ⁐d§¨2ᵫ᜜5▤ᙌC᜜¦ᑁ5▤ᙌCᑁ°±AC᜜UCᑁḄ5ᩩOaᡂḄ.ᵫbx'(C5)=3,ᡠ!j!ᵨ&⁐1(²)*2(¤)*3(³´)'C᜜OḼ⁐*ᵨ3%⁐µj!'¶5ᩩOḼ⁐*,."µᵨ&⁐1,2,

943·4#'CᑁḼ⁐*¸¹º»M%&⁐(☘´)½k../x'=4.17.40.40.¾ᜧ¿ÀÁÂÃÄÅÆÇᙠ¾Èᐳ⌱nË⌱ÌÍ*ÈÎὃÏи¹ÑÐÒnË⌱ÌÍÓὃ.⌕SᜩSÕᙠ,ᓤὃMËÍ*×KL◤⌕ØᜩὃnËÍÙÚCᔣG=(V,E),V={v|v2⌱ÌÍ},E={(u,v)|u,vGVAᨵÕZv⌱Ìu¦v}.122112333339⚪K3,338⚪K4K537⚪ᦣᦪ⚪97ÜÝᑮ*ÍÓuUvj!Zvὃ«àÕá⌱u⌱voᙠGuUv4WXQuUVjYZM%&⁐.b2ãGᨵM%kḼ⁐*ᑣä40⚪éB°ê⚪ᩩë*ᡠÚCᔣG᝞,ìᡠ.GíK3323jḼ⁐Ḅ*./X(G)=3,äu!v"345⁐.GḄḼ⁐894᣸;ᫀ=3ᨵ/5⁐Ḅᡠ⊤Ḅᦟ"#ᙠ⁚(

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