Î÷°²½»Í¨´óѧ1999ÄêÑо¿ÉúÈëѧöλÔÓéÀֵǼÈë¿ÚÏÂÔØ ÀëÉ¢ÊýѧÊÔÌâ
1 (30·Ö)
ÇëÅжÏÏÂÁи÷ÌâµÄÕýÈ·ÐÔ¡£
¢Å 2A¡É2B=2A¡ÉB¡£
¢Æ A/B=Aµ±ÇÒ½öµ±B=Æ¡£
¢Ç (A¡äC)/(B¡äD)=(A/B)¡ä(C/D)¡£
¢È Éè|A|=5£¬ÔòAÉÏÇ¡ÓÐ31¸ö²»Í¬µÄµÈ¼Û¹ØÏµ¡£
¢É ÉèR·Ç¿Õ¼¯ºÏAÉϵĹØÏµ£¬RÊÇAÉϿɴ«µÝµÄ£¬µ±ÇÒ½öµ±R¡ðR¨ªR¡£
¢Ê ÈôR1£¬R2¾ùΪ·Ç¿Õ¼¯ºÏAÉϵĵȼ۹ØÏµ£¬ÄÇôR1¡ð R2ҲΪAÉϵĵȼ۹ØÏµ¡£
¢Ë Éè<P,¡Ü>Ϊ°ëÐò¼¯£¬Æ1S¨ªP£¬ÈôSÓÐÉϽ磬ÔòS±ØÓÐÉÏÈ·½ç¡£
¢Ì ÉèNΪ×ÔÈ»Êý¼¯ºÏ£¬IΪÕûÊý¼¯ºÏ£¬¡äÊÇËãÊõ³Ë·¨£¬Ôò<N,¡ä>Óë<I,¡ä>ͬ¹¹¡£
¢Í Éè<G,*>ÊÇȺ£¬ÔòGÖÐÖÁÉÙÓÐÒ»¸ö¶þ½×ÔªËØ¡£
¢Î Éè<R,Å,Ä>ΪÕû»·£¬|R|=n£¬Ôò<R,Å,Ä>ÊÇÓò¡£
¢Ï Éè<R,Å,Ä>ΪÓò£¬<R,Å,Ä>Ϊ<F,Å,Ä>µÄ×Ó»·£¬Ôò
<R,Å,Ä>ΪÕû»·¡£
¢Ð Éè<L,¡Ü>Ϊ¸ñ£¬|L|=n£¬Ôò<L,¡Ü>ΪÓнç¸ñ¡£
¢Ñ ´æÔÚ7¸ö½áµãµÄ×Ô²¹Í¼¡£
¢Ò ÏÂÍ¼ÎªÆ½ÃæÍ¼¡£
ͼ1 Ìâ1(14)
¢Ó ÏÂͼΪ¹þÃܶû¶Ùͼ¡£
ͼ2 Ìâ1(15)ͼ
2 (8·Ö)
Éè(G,*)Ϊѻ·Èº£¬Éú³ÉԪΪa£¬Éè(A,*)ºÍ(B,*)¾ùΪ(G,*)µÄ×ÓȺ£¬¶øaiºÍaj·Ö±ðΪ(
A,*)ºÍ(B,*)µÄÉú³ÉÔª¡£
¢Ù Ö¤Ã÷(A¡ÉB,*)ÊÇ(G,*)µÄ×ÓȺ¡£
¢Ú ÇëÎÊ£º(A¡ÉB)ÊÇ·ñΪѻ·Èº¡£Èç¹ûÊÇ£¬Çë¸ø³öÆäÉú³ÉÔª¡£
3 (10·Ö)
Éè(A,Å,Ä)ÊÇ»·£¬AA={f |fÊÇAµ½AµÄº¯Êý}¡£¶¨ÒåAAÉϵÄÔËË㨤ºÍ*ÈçÏ£¬Éè
f,gÎAA, ¶ÔÓÚÈÎÒâµÄxÎA¡£
(f¨¤g)(x)=f(x)Åg(x)£»
(f*g)(x)=f(x)Äg(x)£»
Ö¤Ã÷£º(AA,¨¤,*)ÊÇ»·¡£
4 (6·Ö)
ÉèA=<L1,¡Ü1,*1,Å1>ºÍB=<L2,¡Ü2,*2,Å2>ÊÇÁ½¸ö¸ñ£¬fÊÇAµ½BµÄ̬ͬº¯Êý¡£
Ö¤Ã÷AµÄ̬ͬÏóÊÇBµÄ×Ó¸ñ¡£(×¢£ºAµÄ̬ͬÏó¼´£ºf(L1)={f(x)|xÎL1})¡£
5 (8·Ö)
ÉèG=£¨V,E£©ÊǼòµ¥µÄÎÞÏòÆ½ÃæÍ¼£¬Ö¤Ã÷GÖÐÖÁÉÙÓÐÒ»¸ö½áµãµÄ¶ÈÊýСÓÚµÈÓÚ5¡£
6 (10·Ö)
ÉèGÊÇÁ¬Í¨µÄÎÞÏòͼ£¬ÇÒÓÐ2k>0¸öÆæ½áµã£¬
Ö¤Ã÷£ºGÖдæÔÚ¸÷±ß²»Öظ´µÄkÌõ¼òµ¥Â·P1£¬P2£¬¡£¬Pk£¬Ê¹µÃ
E(G)=E(P1)¡ÈE(P2)¡È¡¡ÈE(Pk)¡£
7 (8·Ö)
Éè¸öÌåÓòΪÕûÊý¼¯ºÏ£¬½«ÏÂÊöÓï¾ä·Ö±ð±íʾ³É½öº¬ÓÐN(e)¡¢P(e)¡¢Q(e)¡¢E(e1,e2)¡¢
L(e1,e2)¡¢D(e1,e2)Ëù×é³ÉµÄν´Ê¹«Ê½£ºÆäÖи÷ν´Ê¶¨ÒåÈçÏ£º
N(e)£º eÊÇ×ÔÈ»Êý£¬
P(e)£º eÊÇËØÊý£¬
Q(e)£º eÊÇżÊý£¬
E(e1,e2)£ºe1=e2£¬
L(e1,e2)£ºe1<e2£¬
D(e1,e2)£ºe1|e2 (¼´e1Õû³ýe2)£¬
¢Ù ûÓÐ×î´óµÄËØÊý£»
¢Ú ²¢·ÇËùÓеÄËØÊý¶¼²»ÊÇżÊý¡£
8 (8·Ö)
ÅжÏÏÂÁÐÂß¼¹ØÏµÊÇ·ñ³ÉÁ¢¡£Èô³ÉÁ¢£¬ÇëÓÃÖ¸ÅÉ·ÖÎö·¨¸ø³öÖ¤Ã÷¡£·ñÔò£¬Çë¸ø³öÏàÓ¦
µÄÖ¸ÅÉ¡£
¢Ù $x(ØA(x)¡úB(x))¡ú"xC(x)T"x(B(x)¡úC(x))£»
¢Ú $x(A(x)¡ú"yB(x,y))TØ"y$xB(x,y)¡ú"xA(x)¡£
9 (12·Ö)
¹¹ÔìÐÎÊ½ÍÆÀí¹ý³Ì£º
¢Ù ØR(ØP¨²S), Q¡úØS¨b P¡ú(Q¡úR)£»
¢Ú $x(A(x)¡ú"yB(y))£¬"x(B(x)¡ú$yC(y))¨b "xA(x)¡ú$yC(y)¡£
