最新课后习题答案

部分习题答案及提示第1章．）））72））。）））））．）））））））））））若））若aa。））））））））P）））PQ）Q）））QP）P）P）Q）(PQ)PQ(PQ)(PQ)(PQ)或）P））(PQ)(P(RS))QPPQR)SQP）(PQ)）(PQ)(PQ)PQ．）P000010110101111Q00011QPR0000111100110011010101010111011111110111）0011100111011111P100111011QRA1QQRPQR)P00001111R01010101001100111101110111011111）0100111010QA1PQQPQ(PQ)(PQ)P0011111101010011010001101101）0101111P00QA1QPQPQPQ(PQ)(PQ)P0011010100011100101010001001SQRTQ）P8P）Q8）PQ）QP88PQPPQQPQPQQ；QPPQ；。。PPQPQ；QPQP。PQPQ如果我不热衷于玩扑克（RRPQ6P7被2QRPQRQR或57被2但5RP6．略P）(PQ)(PQ)）(PP)(QQ)）P）F）(PQ)）(PQR)）(PQ)F）(PQ)(PQR）(PT)R）((PQ)R)P）(PQ)R）PQPQPQP(PQ)(PQR)(RP)(RQ)；(PR)(QR)(PQR)PQR)(PQ)(PR)(PQ)(PQ)(PQ)(PQ)）PQR）PQR）PQR）PQR12,4,5,6,7Q；Q0,1,3QP）1,3,4,5,7(PQR)(PQR)(PQR)(PQR)(PQR)=(PQR)(PQR)(PQR)0,2,6.(PQ)(PR)(RS)SQ1.SP附加前提）2.RSP3.R5.PTI4.PR6.PQ8.SQP1,2TI3,4TI5,6P7.QCP(QR),QP,SR,PSPSPSRPPRTIP5.QP)PQTI7.P(QR)P9.RTIQRRRTITIPQR23223（2不3PQPRRQ。，，SSQ,,S,S)D)D)第2章）W(a)W(x)x）T(a)B(a)T(x)）T(a)B(a)T(x)x：：xaB(x)xa：：B(x)xa：）T(a)T(b)T(x)）xQ(x)R(xQ(x)x：am：，2mbxR(x)R(x)xx：：：）x(Q(x)R(x))Q(x)x：）x(N(x)y(N(y)G(y,x)))N(x)xG(x,y)xy：：比x((x)B(x(x)((x)B(x(x)xB(x)x）））或：：(x)((x)B(xx((x)B(x(x)xB(x)x或：：(x)((x)B(xx)((x)B(x(x)xB(x)x：：或中M(x):xF(x):x为长头发。则符号化为：x)(M(x)F(xS(x):x(x)(M(x)S(xD(x):x(x)(M(x)D(x4令Q(x):xH(x):xxQ(x)H(xB(x,y)：：(xy)((x)B(x,y)(z)(D(z,y)C(x,z)))(x)xxyC(x,y)xyD(x,y)xy是：是：是）(x)((x)B(xx)((x)B(x(x)x：B(x)x：）(R(a)Rb)R(c(S(a)Sb)S(c）(P(a)Q(a(Pb)Qb(P(c)Q(c）(P(a)Pb)P(c(P(a)Pb)P(c“）(x)(P(x)Q(x))）xy)(z)(u)((P(x,z)P(y,zQ(x,y,uxy)(z)(u)((P(x,z)Q(,y,u(P(y,z)Q(,y,u）(x)(yu)(r)(z){(x,y)[Bu,r)((z,u)Bu,z))]}）x)(z)()[(P(x)Q(z,yR(x,x)(z)()[(P(x)R(x,(Q(z,y)R(x,．（设W(x)：x，B(x)：x，R(x)：x该命题符号化为：xW(x)B(xx(B(x)R(xR(x)W(x)证:(1)R(x)(2)R(a)P(6)xW(x)B(x(7)W(a)B(a)(8)W(a)PES(1)US(6)T(5),(7)IEG(8)(3)x(B(x)R(xP(4)B(a)R(a)(5)B(a)US(3)T(2)(4)I(9)xW(x)Q(x)：x是有理数，R(x)：x是实数，Z(x)：x该命题符号化为：xQ(x)R(xxQ(x)Z(xx(R(x)Z(x（2分）证:(1)xQ(x)Z(xP(2)Q(a)Z(a)ES(1)（1分）(7)R(a)(3)(8)R(a)Z(a)(6)Z(a)T(2)I（1分）T(4),(5)I（1分）T(6),(7)I（1分）Px(Q(x)R(x(4)Q(a)R(a)(5)Q(a)US(3)（1分）(9)x(R(x)Z(xEG(8)（1分）T(2)I(4)第3章3.1．）；）2,3}；）；）i5i．．n}）{5,6,7,8,9,10,11,12}；n{x}．．．．．）{,{}},{a；}}；,{,{；{,{；）{{},{},{},{x,},{y,},{,},{,y,）．a,a}Ba,a,a,a,a}a,a,a}Ba,a}B．B，，，1748314567826770181293.4．ABC{,,,}；A．B{,,,,,,,}；23.5110M000S{0,0,0,2,2,0,2,2},domS{0,2},ranS{0,2}．，S110100000MS，{,4,2},domSranS}000S010．PUQ{,2,4,3,3,,4,2},PIQ{2,4}，PQ{,,,domQ)dom(PUQ)ran(P)ran(Q)ran(PIQ)L{1,2,,,2,2,2,3,2,6,3,3,3,6,6,6}．D{,,,,2,2,2,6,3,3,3,6,6,6}LIDD{,,,,2,2,2,6,3,3,3,6,6,6}．223.6．）Y)的给出证明，对每一个非(N)．RURRIR121212YYYNNYYYYY但NYYYYY2,R,．R；RR2,R,RR1233344R但。410010000．M，1101R0010a,b,c,d}X，RRXn(n2232n2）n2））n）？n2n2到YXRR否12）RRRR1234),{}f({})f({,{}}){{,{},}，，fa,fa,b,fa,b,c,d，，，DDffffDffD2ff[0,],R[0,1]DffDff（2运算gxymaxminx是否是是否是Z表o表102301234o1234112342234333444442343694801234501234567670012345012345600000000123456024613503625140415263053164206543211234566012345123456234560345601456012560123601234(a,b),(c,d)AB(a,b)(c,d)(ac,bod)AB是ABA,5.2a,bc,cb可交换，不幂等，有幺元aa1；11ab,c，ac，aa1br1c,cb；1l,b,ca,b,c；a；，aaa1，无aa1运算是否是是否是是否是否否是否是否否是是否否是是否否oSf(x)f(x)f(x)f(x)0123f(x)f(x)f(x)f(x)0000f(x)f(x)f(x)f(x)f(x)001231f(x)f(x)f(x)f(x)f(x)23210f(x)3f(x)f(x)f(x)f(x)3333(x),o,o是SS1和11121122S，yxxSx记xyx(xx)(xx)xyxxxx。abc)ababacababc)abac而故bc)ababacababc)abaca而故,(ab)dadcabd)aab)。Z,Ao,对o，,)(oR,oo．,。a1N,1A。666,0},,0},S,和是S,S,g,ii1010。0101110无左幺元，右幺元为1010S,g。3S,g5。0000S,g60x无左幺元，右幺元为0100x10000,g,iS,giSi习题5.4Q,aQ,a．是群，因为运算“a4/a1。Z,a4a1。a1001S,f,L,fo{f126ffffff1234ffffff512345123456ffffff3f2146ffffff6f3512ffffff5f4621ffffff1f5364ffffff2f64531off，，f12f，f213f，f314f，f51514f1f{f,f,L,f66126HK,G,设是H,K,HK,G,都是子群，并从khKHHK的定义及，由，，hkHKkh(hk)；11得111HK,G,(hk)khH,K,，hkHK是111由G,(hk)khhk111。HKKH。对x,yHKh,hH,k,kKxhk,yhk得12121122xy(hk)(hk)111122(hk)(kh)121211h(kk)hG,121()112h(kh)K,12)1h(hk)HKKH（）133(hh)kG,（133hk3HK,x,ygxghg,yghgg1，11112xy(ghg)(ghg)gh(gg)hg11111112121g(hh)gghggHg11211，1gHg,G,故1是ezyexSySyxeySzS，xye(xy)(zy)(xy)z(yx)yzeyzyexSxex(yx)(xy)xexS,S,e是xS习题5.5(R),M(Rg．M是Gx3x2eyxyx，x1且xyyxe。,．G44555314G13,33,43,53,932是在5143G,5和97．和。dc{,,L,}Gdnaaam2mdm习题5.6,}a,f)a,f()A{,},U,I1．是。因为f是到a,U,I．fZ,到gf(31fgf0。Ba,b,}fP()P(B)，A，，令f)f()B,fa,f(,}则f是P(),U到P(B),UP(B),U的幺元是P(B),I的零元是f(P(U}fP(),IP(B),If(P()),I；到是}。）fe0xg{或abia1,,},gabRZ。2b22ixm,nZ,n．f(mn)1f(m)gf(n),n当mf(mn)1f(m)gf(n)f,g()}g1是RfnnZ。。x,yG,f(xy)1/xy(1/x)(1/y)f(x)gf(y)x,yG,xyf(xy)2(xy)(2x)(2y)f(x)gf(y)。x,yG,f(xy)(xy)xyf(x)gf(y)。222．提示：是，因为x,yZx2,y2,k,lZklf(xy)f(2)1f(x)gf(y)kl2或y2,k,lZ若xklf(xy)0f(x)gf(y)f对x,xG,若f(x)f(x)1212axaaxa1112该式两边同时左乘a及右乘a,得xx,故f为入射f.112fyG,都存在xayaG,使得yf(x),因此f是满射.对1f最后,对x,xG,都有f(xx)axxa(axa)(axa)11112121212f(x)f(x),f的自同构.12(k,G)1,mnZnG1,xyG14f(x)f(y)xyxyG,xyekkmkmkGGxyfG,fxmknGymknGx,yGf(xy)(xy)xyf(x)gf(y)，fkkkf是G,,Qg:{0}fQQf(1)0f(1)f(f((1)(1))f(1)0f(1)0ff,Qg习题5.7{0},H,．C是axxC,xa，aHa．1。2。3。NN。666．nZnknZnikiZ},kL,n1。,yH,x,yG．H{x0000x,yH{xx,yaxx}0000,yxaHa00SS,，eeSeHKxHKxHK。HK1Ga,bHUU使GHaHHHb。gG,hH，g1hgHgG,hHgHg1hgH。H()()()hH使ghbghghbhhbbhhhbH否若g1111111111(hhh)bHbb(hhh)H(hhh)b(b(hhh))Hb11111111111111111。习题5.80习题6.1(ac(e)b)b和de(d)bc(f)fg3,|．L,|,,,．LabababL,,L,,L,,,L是1343S,|6，6,|S6。。6.,LUB(M,N)(max(m,n)),GLB(M,N)(min(m,n))。Aijijijij设,L1,{,}Lab，bLabaabb或或,baabLa若La,,}abcLLaabcLL是是ba,的最小元，不妨设为cc习题6.2习题6.3习题6.4))2n,b)a)2）n）c,,d,fbb(ac)。）a）c）a设B,,,,0,1B3B，a0a1a11,但a1a0，a0a0a1aaaaa故a在BB,,,,0,1bababaaaa()()()()000a(ab)(ab)0ab00且abaa(ab)(aa)(ab)ab，bb(ab)(ba)(bb)ab，ba。ppLpp,pL,pS,|是rn12r12rnB,,,,0,1,BabBab(ab)(ab),,,,ababab)()AA“a,b,cA，(ab)cab)(abcab)(abc)ab)(abc)(abc)(abc)ab)(ab)c)(abc)(abc)(abc)(abc)a(bc)a[(bc)(bc(abc)(abc)(abc)(abc)aA，a0(0)(0)(1)0aaaa0a(0a)(0a)0(1a)a0A，aAaa(aa)(aa)000，aa。1）a,bA，ab(ab)(ab)(ba)(ba)baA，B,,,,0,1Bg,abBab(ab)(ab)ababB,g,B,,,ababab)()AA+”a,b,cB，(ab)cab)(abcab)(abc)ab)(abc)(abc)(abc)ab)(ab)c)(abc)(abc)(abc)(abc)a(bc)a[(bc)(bc(abc)(abc)(abc)(abc)aA，a0(0)(0)(1)0aaaa0a(0a)(0a)0(1a)a0是,aAaa(aa)(aa)000，aa。1）a,bA，ab(ab)(ab)(ba)(ba)ba,gBB,,,gababBB“ga,b,cB(ab)c(ab)cabc)abc)，gg故Bg+对a,b,cB，a(bc)a[(bc)(bc)](abc)(abc)gg()abacabacabacabac(ab(ac))((ab)ac)(abc)(abc)abc)abac又a1a11aaa是B,g,g0a,fff(a)a0f(a)。(a)yB{,f(ayf(a)f若fB满足x0,axAyf(x)yff(a)ff(x)f(a)，0xaa(aBf习题6.5(xx)）x；；123x）x；12(xx)x））；123x2x）x；12x）x；12(xx)x））；。123(xx)x132(xx)(x(xx))x(xx)2312123231230000110011000101010000011001100010101101110100111111011111110111(xxx)．f1231,3,5,6,7(xxx)(xxx)(xxx)(xxx)(xxx)123123123123123f(xxx)xxxxxxxxx()()()123123123123(xxx)f123(xxx)(xxx)(xxx)bxxx)123123123123f(xxx)123(xxx)(xxx)(xxx)(xxx)bxxx)123123123123123习题6.6．第7章G)(G)G)）k==(a((cb010101110212001102010122AA，）A）2301010110212010000