ÍÏÍ³ ÇÌÂ Ì ÍÏÍ³ Å ½ Ì ¼ (1) (5) Â µ ½ Â µ Í ½ (1) ¹ (2) 77 Á (3) º¾ Á (4) ÀÎ 2017 (5) x+y xy <!-- Ì!"#$ % &' ()Å* + Ä², ¼ 2 Ï-». /Ï- *

Bản ghi

1 ÍÏÍ³ Å ½ ¼ (1) (5) Â µ ½ Â µ Í ½ (1) ¹ (2) 77 Á (3) º¾ Á (4) ÀÎ 2017 (5) x+y xy!"#$ % &' ()Å* + Ä², ¼ 2 Ï-». /Ï- * É7 8 49: É; ÍÏÍ³É7 8 6 ÍÏÍ³9: É; 1"#$ % &' ¼ (1), (2) BC DE m, n, k f FG H L, (1) nm2 Nm (mm2 mon P Nk nqkm) (2) Nm Nn (mqn P f(m)qf(n)) RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR SBLST U

2 x y xy É¼ Ê ÏÍµ¹» É (1) (2) (1) À Äx, y x-y! ÏÍ É "#À z $%z!z! z: z: É (2) Ä &# ¾'("# 2k É À 2k+1 É À )* +,-Î. /0 ¼ Ê ÏÍ É (1) x1-1 x11 (x+1)x(x-1)10 23 (2) x13, y x+y15, 2x13y ² 7² 8,-Î. /0 À x y x ¼ y! 9 : ÏÍ É Ì1»" µë 7) ; µ¹»(. <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< ²Å ²=

3 Ì À ¾ ÏÍ¼ Ê ÊÀ Á ½¹ x y Î²! "Ì# $Â (%&')(('&%) )* +,Ì)Å- (1).$Â/ÍÉ 01 (2) 2µ$Â ÏÍÆÃ3 /ÍÉ45 6$Â 78- $Â 9 µ: º;< 478. "Ì (1) x y. É µë x=y»> +?Ä ÏÍ¼ É@ (x-1) 2 A 4 BCD EF x * (2).?ÄG*. HI@-HIJK3L MNL OPQ6 IR. "Ì STU VW1X À Y) +Z$Â Á[ \ ]^ _ µ:»>ïí¼ É@ (1) `a x )* xbx 0 c2 (2) 9 xbx dp x ]^ (3) (xe1)b(xf1)gxbxe1 hd¼ (4) Ji¼ xb(xf1)g0 jk ² (5) Al mnëo jk (6) 4 3bxby ) É@* "Ì STU VW1X Ì (1)ÏÍ¼ µ:=»pq)3yµ:b»>6é@ rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr ²Å ²s t

4 ¾Î Ê Ê À ½¹ U {0,1,2,3,4,5} P(x) (a) x 5 ² (b) x 0 (c) x (d) x 1 Å (e) x É ¹¼ ÌÂ (1) P(x) x ½¹ {x U P(x)} Á µ ( P(x)!x Á "# {2,3,5}) $%& (2) '()Â *x P(x) +º,Â -x P(x)./ :; <=>?@AÄBx CD=4E@FGH x.ijcd=4e@fg. KLMNOP4E@QCRSTFG1UVW78UVJX1VY?@FG8 Z[\UVÃ4B]=4E@FGCD=4ZTFG.KLMNOP4E@Q GT^<=._`1»ab7T8 9:c d. (1)e(4).,f1ghi4jW8 Z[\klmnH<=op.qrGSstuv xwx y ywx z.vyh{l4 \ x C y.}=4e@fg1 x y Gj?8 (1) ~.<=\IJ?@GR4E@8 (2) IJC N >zst<=c+º?@8 (3) x C]=Z ƒ\x H. =4E@8 (4) E@]=H\.IJC 4 vˆ ZT8 9: Š Œ.E@ Ž (1) ghæ Z r,f (B G. Q.7^>56@)8 (2) t. r,f G š CghÆ.G.\ Æ,f œš./hj. ž1ÿ 78 5G

5 Â Á ( ) ÏÍÆÃ Í ½ S É! À % ÏÍµ&'(»)*ÏÍ¼É! Ê ¹ S É x Ê ½ x ² " Â S#$ +,-'(¾./ 0 1 Îµ» À (1) Ê (2) Ê /9-È: (3) : Ê ;º<- (4) =-Ê ;º >? " GEI¹ÏÍ¼ JÄ/KL0MEF3 (1) Nx x^2#x (2) Ox x^2p0 (3) Ox (2 x 4 x) (4) Nx (2 x Q 4 x^2) *R<5678À ¹ <x^2 x ÊÉ STUV WXYZ? [\]&JÄ ^»)*ÏÍ¼É<EF! EF _`abä<.acd eff3 x y =--CDg- z 5<./ z x y h-d /i = jk Èl¹ mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm nå no p

6 ¼ Â ÈÄ ÏÍÆÃ Â Q(x) ½ (1) (2) (3) x (P(x) Q(x)) (4) x (P(x) Q(x)) ¼ Â ÏÍÉ µ ¾!¾"# ÏÍ$¹%Ê %(À )Ä &' (Å¹ ) %* $¹»+,#-. /0Î À Á x78 Å 94:; - (1) <À =>? '@ - (2)?A À '5-,@ B=> < CD E '4 FG HI'C- DJKL <MNO À ' 4¼ PQR-S ¾"# DE4 T ' U,@T ' VJKL <MNO (ÆÃÊ '#W -¾ 09XY ZË[\ ]^) 23 A, B '5-, ¼ _`a6b5s ÆÃÊ '#6¾"# AcB d e A f B^c SS X^c X g23 É4 hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh ²i ²I j

7 ½¹ A, B ¼ À Î ¾ A B ABA Á ¼ À ÌÂ Å 0X nx n2x (1) Æ À» Ë Á ½¹ X!Æ " (2) # $%½¹ $& Ê' º( ) {n P(n)} * É +, P(n) -Á n. / ½¹ {0,1,2} 8. R R(x,y) : (x+1) mod 3 y mod 3 Ä9 +, m mod n - m n :;< 1É (1) x y = >?¹@ R(x,y) ABÃ ÉCD (2) ¼ EFÂ AµÅGH%¾I (a) JxJy R(x,y) (b) JxKy R(x,y) (c) KxJy R(x,y) (d) KxKy R(x,y) L (1) M ½¹ X, Y ¼ Æ À Î (a) XY Kx (xx xy) (b) X Y Kx (xx xy) (½¹ NO ÄP) (½¹ Ê' ÄP) DQR< M ½¹ A, B ¼ À Î ÃS* ¾R< AB A B W B A TBUV" (2) M FÂ X, Y (XWY X) XY TBÃ:3 ÃS*R< ¾ ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ ²Å²[ \

8 ½¹ X ¼ À Æ» Ë Ê º¾ ½¹ µå Ä 1 X x X 3x X x X -x X (1) ½¹ X Á Î (2) X {x P(x)} Ë P(x) Ä!±å "#$%& ¼ ' ²Ä() S *+*, -. (PQ) (RS) R (PQ) R / !±å "#$%& ¼ 89Â :Ï *, (1) P;Q P<Q (2) =P<Q (PQ) BC D EF ²ÄÈG HI+J K LM 0 1 NOP QR ST U LMV ½¹ L {0,1,01,10,010,101,0101,1010,W} µå Ä XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX YZY[ \

9 ¼Á±å Æ½» µ ²ÄÈ¹ (P Q)(Q R) P P Q (P Q)(Q R) Q Q R R P R (P Q)(Q R) (P R) Â PQ (P Q) ¼Á±å¾ $%&Î ' ()!"# Â *(P*(P+Q)) ¼Á±å¾!"#,%&Î ' () Ê- 0 1./ "9:;<=43>?@A BC DE6"FG HIJ, 101, KLMABC DE6 NO 10, 011, , KLMABC DE6KP. K 6É2 BC DE6 QRÅÄSTI UV"UÀ W

10 ÍÏÍ³ ÇÌÂ10 P Ê ½ µ¹( Âµ¹) Q Ê ½ µ¹ ¼Á±å ¾» ²Ä I!"#$%&' Ë()* +,-.#/ 345 P xq(x) 0000 Q(a) P1 xq(x) P1Q(a) P1Q(a) P1Q(a) x(p1q(x)) P1 xq(x) 2 x(p1q(x)) (1) À&6 (-789È &:;º(-<=>?@: &#$AB<AC +DE)FE)G#@É/x : &HI-.# P(x) HÉ(/ (2) JKF78FLM NO6P(/.Q RSTUFLMV#@É/ WLMXÈ &:;ºYZ?@: &HI-#²Ä[\ Æ]/ ^_F²Ä`aÈ &:I-Y=bQ a #c]#a $ &H$<A/ ^5F²Ä`a?@: &<FHa $ &HI-/ a : &H$<]Yda : &HI-#A"[\:ÆYQ/ 34eWfÎFI-ghiX jfk786za@lm<=>rstuhlmnohi-.# lmh<a<=>78:p#<-m)ãfqaå@ (1) ((P2Q)1(R2S)) 2 (PtR 2 QtS) (2) ((P2Q)t(R2S)) 2 (P1R 2 Q1S) rzsb`/ P 34uWfÎFI-ghiX 5%&F &Kv max, min #%&Kv i, j #Ä&Kv 0, 1 Y=w=Qx jf`"6yz{6ä -/ } 0, 1, i, j $?@xhi-/ } s # t :x<=>max(s,t) # min(s,t) $~6xHI-/ (1) x6q- &Kv#Ä&KvF & - & sym jf (a) (c) H Äƒ(-/.Fyz{Äƒ6 A@sym(max(min(0,i),min(j,1))) FÃ (a) sym(c) = 1 (c : 0 Y 1 F#) (b) sym(x) = 0 (x : i Y j F#) (c) sym(f(t1,t2)) = 1 + sym(t1) + sym(t2) (f : max Y min F#) (2) x #@É(#F Y=ˆ HFŠF Œ xfž # / B>x 1 FŽ $ x max(i,0) FŽ $_x min(max(i,j),0) F `/ Ž $5HI- OV /xfž - & height Fyz{Äƒ B`/ min / \ max max 0 / \ / \ 1 i 0 i j s# š

11

12 ÍÏÍ³ ÇÌÂ11 ¼ Â x P(x) xp(x) Æ Á±å ¾ µ Å Í xp(x) x P(x) P(a) E E,3 P(a) P(a) E! I,2 xp(x) I,1 x P(x) xp(x) " Â ( P Q) (Q P) Á±å¾²#$ % &'(Î )*+, ¼ -ÏÍ.Á±å¾²#$/Ã0(EM)» % (1) x(p(x)1q) ( xp(x)1q) (2) xp(x) x P(x) 2'(Î )*+, Â3¹ P, Q 4º45 ÂÏÍ ÏÍ. ¼ Ä:; <P, Q ÏÍ. <=>ÏÍ.?4@ =A>, =1>, = >, = BÏÍ. Â3¹ P, Q CÍDEFGHIJÉDKLMv : {P,Q}N{0,1} O P 789Ä: FÉD v Ä:QÏÍ.RS TU5@ VW ÏÍ. CÍDÉD v X Y; v(=a>) Z min( v(=), v(>) ) v(=1>) Z max( v(=), v(>) ) v(= >) Z max( 1 - v(=), v(>) ) v( =) Z 1 - v(=) [@ Q \ ; Q C $ Q ] CÍD EFG v v(q)z0 Ä^ v( Q) Z 1-v(Q) Z 1-0 Z 1 Y $ Ç; (1) Â P 1 Q PAQ CÍ_J`Ãabcd M½+ (2) ÉD v v(p)z1, v(q)z0 Ä^ÉD v e P1Q PAQ CÍD v( P1Q PAQ ) Ä: X Yf (1) ab»gy% (3) ÉD v v (P)Z0, v (Q)Z1 Ä^; v ( P1Q PAQ ) D h^jdi+h^5@ `Ãab jkm llà N

13 ÍÏÍ³ ÇÌÂ12 ÏÍ¼ x R(x,f(x)) x y R(f(x),f(y)) Ï Á±å ¾ Ä c Ê µ¹ f Ê ½ µ¹ PÊ ½ µ¹ R µ¹» Î U ÈÉÀ! "# $µ¹ ²% [&] [c] ' 0 [f](n) ' n+2 [P](n) ' if n ( then 1 else 0 [R](m,n) ' if m)n then 1 else 0 *+Ä, $ÏÍ¼ -U,[&]. / 0 12 Í3 4½5* (1) P(f(c)) (2) y R(c,y) (3) x y ( R(x,y) R(f(x),f(y)) ) 6789 : ;<=> ÏÍ¼ x y AÎ ²%B C D789 : ;<=> ÏÍ¼ EE x P(f(x)) y P(f(g(y))) Ï Á±å ¾ FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF ²Å ²G H

14 ÍÏÍ³ ÇÌÂ13 ¼ ÏÍ ¹ ½ (1) xy R(x,y) y x R(x,y) (2) y x R(x,y) xy R(x,y) ¼ ² ½ (1) xp(x) xp(x) (2) xp(x) xp(x) Î! ¼»" # " Á$ %&±å'¾() %&±å'¾('*+, -.Ã/) (a) x R(f(x),x) x R(f(f(x)),x) (b) x R(f(x),x) x R(x,f(x)) (c) x R(f(x),x) x R(f(f(x)),f(x)) (d) x R(f(x),x) x R(x,x) 0Î! ¼»" # " Á$ 1 µ+23 4) ¹ + -.Ã/) (a) x R(x,c) y x R(x,y) (b) xy R(x,y) x R(x,f(x)) (c) y x R(x,y) xy R(x,y) (d) x R(x,f(x)) xy R(x,y) Å6À 7

15 ÍÏÍ³ ÇÌÂ14 Æ½ Í» ¼ ÏÍ ¹ (P Q) P (R S) (P Q S) (R S) Æ½ Í» ¼ ÏÍ ¹ xr(x,f(x)) xy(r(x,y)r(y,x)) xyr(f(x),y) ÏÍ É ¼ ÏÍ wxyz ( R(w,f(w)) (R(x,y) R(y,x)) R(f(c),z) )!"#Î $%&' ¼ () ÏÍ *+ ) Á, -./0 -.²0ÏÍ 1 Ã23 (a) xp(x) xp(x) (b) xp(x) xp(x) (c) xp(x) xp(x) (d) xp(x) xp(x) 4"#Î $%&' ¼ ÏÍ ¹ (1)Æ½ Í (2)56±å Ä7 ÊË xy(p(x)r(x,f(y))) xp(x) xyr(x,y) Å9À :

16 ÍÏÍ³ ÇÌÂ15» À { R(w,w), P(w) }, { R(x,f(y)) }, { P(f(c)) } À½¹ ÆÈ Í Ê Å À ¼ ÏÍ Éµ x (R(x,x)P(x))!"#Î $ %&' xy R(x,f(y)) x P(f(x)) ¼ ÏÍ()*+$, Í-./ 01 x R(x,x) x2y R(f(x,x),f(x,y)) 3"#Î $ %&' Í45¼ ÏÍ()*+$ 6.78 x2y R(x,y) xy (R(x,y)R(y,x)) y2x R(x,f(y)) ²:.²; <