Toán rời rạc

KH-?,IH-LH.M2222222222222222222222222222222222223N$

%&)G' 22222222222222222222222222222222222222222222222223N$

% O1222222222222222222222222222222222222222222222222223A$PQH-RH.M222222222222222222222222222222222222222222222222#S$

%#0"T" )U 222222222222222222222222222222222222222222#B$

%B4056C4D EVW52222222222222222222222222222222222#A$EF")GH-?,IX22222222222222222222222222222222222222222222BS$



0"Ti.LHop)1cEF")G'222222222222222222222222222222222222222&&#$

012456789 



   1 0

!" #$%# &'($ ) * ($ +,

-./950 567584 10.D?98EFGH3;D8?I;J8KM5N8?O8KP?Q8K4?RST5;J8KUTVWVCX21A ;D8?8?OU[\;O]A52C_`abcdef2

1A=>8?;@;J8K;O]A9BC_ABghi jlmcnbdopdeqbrd tuvw jkleqbrXxA1A=>8?;@WVC

;O]A9BC_ABtuvw jklyzh2

=‰0W9567Ž9A;D 0VWŸAB=‰0=>8?;@ S”C ¡VAB=‰0

;@;J8K¢£¤8KP?NU”C ¥VAB=‰0=>8?;@WVC2 ;D8?8¦\;O]A52C_=‰0§l

j¨S_A©8KE¦;NO]9 W10AªV^/5CA2

«54?O…95Y¬>6A1A=>8?;@‡­CA1A ®¯°¯±¯²S_ 0.D;J8KIM5N³;O]AY¬

>6‡­N´Iµ³¶·QN VA¸9•¹95A1AY¬>6º¯»;R  0.D;J8KU¦½•R  0.DWVC2

0 YÀA1AS¿•Á0V0 A1A=>8?;@;O]A V.V^_=Œ^/†C

À1A=>8?;@;O]AĐ7•Å950 CŽ9Y<0 †C

‡ž95A1A^CŽ90TsS_x 9<6Ç0 †950 -V9BCA1A

=>8?;@9_7^_=>8?;@ {|}~(ÈÉ.…N;ʖjuËQN;N“†/^_=‰0=>8?;@  

À1A=>8?;@ 0 Đ7•Å950TA1A=>8?;@ ‡ž95A1A^Ž90T

0.†950 -V9BCA1A=>8?;@9_7^

A–2{|}~ 9V70.…N;ʖx›™^_W9567Ž90^_A1A=>8?;@9567Ž90 

.AªVA1A=>8?;@;Ì8KN—8?Ì8U¦3H3Ï?ÐÏ8C9_70 >9Ñ6V^Ò90T 0.†950T 

ÓÔÕÖ×ÕØÙÚ

ÛÖ×ÕÕÖÜÝÞØÖßuàelwu >6‡­Cá®I;2A^ #âã

0DAªV ®_’9<6 0.DAªV®E¦´U¦8KO]A^†C2

-VAB‡—95WV652C_äåwg tuvw jlAªV ;D 



Š‹ !"#$%'(%iŒ(*+, ./0123456%389*:;/6<=->P2A3B*CD5%% 7FG% KL*+,%>@%CD9M6*N>C KLŽS2TUV0W2XYX2ZU8[95

abcefghijklmkcnokpqrkstkuvwxyghzx{gh|xyghfg}~€ 7B9 ‚9,-K+1P3$=



!  =68 1P%3–PD]3Å<B6­5*Ž95L*‚9 ’6Á9NW7 ‚K!Æ'­K-L*!

! , -5*Á6L* ¢‘3]ƒEY3]P%R95¯FÇ955*Á6L*‚9'Á' L" HÀ12312%R<31\<3$IÁK Q96,-5*Ž95L*‚9

012456789 

 !"#$%9&6'(*+,#!-./0123 617'8 *90:!-#$;017' >' 9&6*?#"@A#B#C,#$3%646 90D!#+,#$E$F0G*H2 LM9N %6'Q*<7*Q'$%R#$S!-#!T!#!&6'$S!-#U")*0:!-#$S!-#+,#!-./0123VWX#$Y#UP0GZ[\]^_`a\^bd0EP 4fK(  %6!".#g@Rh

…†0{0 !"#$%  !"#$%H2

…†0{0|6&9 !"#$%¦>§>0G( 1Ž756{(L70{0 !"#$%!,X#$YV

…†0{0 9z6 ({0(LM90{0  !"#$%<7|6&9 !"#$%( ‘( (‚

#$ ¨$©A#U"}(‚$./~#ª˜~#$ |“60{0ŽR#«¬­›#$F L® 9z6 9(LM90¯e !"#$%!,X?#$S!-#w@#C,#UwT!#~˜~#Z°±²^b³_^_´\97K2µ¶·!".h

¸¹¦>§>º»¼½¼¹¦¼¾¼§»¼¿¼¹¹Àº»Q¦»

17‘(295 !"#$%UwX!-#$Y#¦>§>º170{0|6&9 !"#$%0Á9'17‘(

 !"#$%2

06Oy¸>Ã17ā295 !"#$%N Ž7À¸>¸¼¾¼Ã>¸QÃ>¸8 Ã170{0295 !"#$%2Ő95 977(P0G( €7‚!-#$./00{0295 !"#$%079595770795 (2e2

ƯU#Ç"˜~?#$3%R#U@#ÈR@!#U©™#$z6<É6‘(295 !"#$%¸¹¦>§>º>» L0EP

 !"#$%$Y#~Y#$./0¸¹'>*>Ê>»¼  0{0|6&9 !"#$%¦>§>º>|“60{0  !"#$%'>*>Ê> Lª˜~#$ @#C L0EP¸¹¦>§>º>»

L0EP¦>§>º> ( 90·( ¦>§>º>”6P0{0 !"#$%06( '>*>Ê>4G6 ‘(295 !"#$%¸¹¦>§>º>»0G‘( L{0

$!"#UwX!-#$Y#™Í6 &( L0EP¸¹¦>§>º>» L0·(

¦>§>º>

012456789 

46 9   6 !

"#$%&$'%()*+,-,./&019523456789! ;6<95= 234>96>?59:

 B3ACD4EF7 G>H 52I J3A3KE>9: ;6<95= 52

L47M49!N@95>M7O3A7O3APQAERST5! VP:59: ;6<95= >G:>

€Â&‚Ê/&Ô?Ơ†?Ưˆ7O3A7O3APQAERSTÔ?Ơ‰†ÀƯˆGkN95K‹E6 s

78  \j0195234M7O3Ao7O3APQAERPŒ‰†ÀƯ2

"#$%&âr&đêôêô&ơẶ6796•5ư/GT—†—Ư9:]\9234}đ9: B3ASŒẨ9:

[6 ẪVEàXVRKRÁRM7O3A7O3APQAERẬ

IJKLMNOPLJQNRST59UTVW XZW[\]8]^95_67`6aW`b59TW agdU95

W[iTj\ 8kTjlmnopqrmRopqrmstruvw

x: yz{|}~N€QN

5wx4yelk&g&…

†S‡@QAV9U7:TUAV3 [4ˆ9‰cˆ9., qcˆ., ers"cˆ9., krsŠ>V9U‹@7:TUAV3 W[ 4ˆ9‰ˆ9., qcˆ9., ers"

‰ˆ9., krs95"#gŽ>Š‘:A7:TUA3 W[ 46’6€T

“OPAVQ”‡79A57-•4ˆ9 W !" $%&&&'()*&!{•

4ˆ99–+~4w4UA:TU:TU7y95— 9 $%&&&'()*&!4

6’6€T™š95 S7:TUAV3 W9x GPUA:TU:TU=9U@7Ž—

  $%&&&'()*&B$%&&!&'()*&ED2›”‡=M€7+ œ $%&&BC!D&'()*&E@:G4

 $%&&!&'()*&B$%&&&'()*&ED+,95"OP+94ˆ9‰c 

‘:A 49 .žPUA:TU:TU=9U@7@ 9q615 

C!&"!C!2

        

 95!"# !& # '9 *6+# -!"#./ 56274582349:;49<;=;49245(&?#@245@)A',BC95$'$D67#E$.67B&8245F.67A >H$IA!"# 56 D!?

#A5(&?0J#6K924L& $'$D67#E$.67B&8245MN$',BC2345F.67AD>? D6P

> 5&$$IA,Q49<Q=Q92;47RS42TU4VWV74X7WV4YZ95!O2745@

V7„UŒ;4‚245Z#!r9# '9p&Z$Ž# $'$m&J9!O2745@\en4‘7M4{K7$'$#@245@mG75&p

R4ˆ?#-$'$#&@245@.67A!"#./0J#>6K24hiu2343UR24h #&J,#C$',BC95$'$D67#E$.67B&8245F.67A0J#6K2n4œF#O9A!r 675U89#}„45ž.A6€

 5695 



 !995"#$%()

*+'5&(),167$#) !995"#$%,-96.9 !5' 2 /94(69).6 06!6"#

)0

[_a`fg!669h!9U99e

! 3N4OCP996:99:Q9 B69R9S

T 3

! UVH;IWXWWYCZ[\]^_`ab$cdeb$fgh'$Ci+* G9EF Ck;I

lm1no p

q sY5t67*u+9T79T  sxCk;Iyz{95 +6* (|7}5~T*}€95

yz{95 CCi+ CZ 9T85 }{95 +ƒ99y…Ck;I†

  !"  5# &'&( (67+6,!-./01"2!34

956:8:6;8

7X97YZ Y[8

\I"@]IPO!3PAPP#9  H_!B.!"`/01"2!3a

bcdefghehijklmnokpmqprsmqtuvwxeiyze

  £2



US`F6G9EWWX9aK;\&bAK?EWc -I;EW5I?\&ef(:gS  + \&C*i&j=(\&eRS k\&+*X9alEW2 :7< \&S X"-A\&enB-o 5TUVp955_ Y9ZW9

FI$rst/rut6rst;ruLvwLrseRn-A+C x95 %&'( )*+,&- &y$rsz5I8952 5{/ruzc5)8952 9:5{6rszc8952 93>{;ruz5I5)@&'(g(AB+C8{?rsz2

012456789 

0 "#9$%$&2 ()*+,*-*./0195 45 7789:

;<=>?@ABCDAEFA  "H 9J7K8!95&L*M*N024OPQ*NRNSPT*UV

;<=>?@ABCDAWFAXY5Z8U$%$&U OPQ*NRNSPTLY5Z8\$%$&

\OPQ*NR92

;<=>?@ABCDA]FA  "H J7K8!95UL*M*N024OPQ*NR9U2

4#^* OPQ*NR_X`$%$&abOPQ*NRNSPTc*dOPQ*NRPe)*N024GKO6"Hfg$%$&ahc*iQ0*.Q#OPQ*NR9799#^*./0195 jQM)*./0195 k77892

¡¢75197  "#9a£X$%$&a£$%$¤2 (79#6 

"¥95 4YN J7KU$%$&$¦§¨$Ua£$8H  #9$£$%$¤9—9945 0295 #9£ OPQ*NR_g£$%$¤aUa£b_r£$%$¤aUa£b2¡¥PT*+•+Q*Pe)*  "#9$%$&©$˜g£$%$¤aa£™

˜r£$%$¤aa£™24#^*0295 9tN024«OPQ*NR:

g$%$&ag£$%$¤a$a£fr$%$&ag£$%$¤a$a£fg$%$&ar£$%$¤a$a£fr$%$&ar£$%$¤a$a£f

¬0­PT*PQ~®P*.M*+,*.Q60295  "#P*¯*./0X48o "#P*)*°M^*N6N024«

OPQ*NR992 8!954Z4OPQ*NRN,±bg£$%$¤ag$%$&aa£b20

NRPe)*NSPTc*²^)*/M*³OPQ*NR_g$%$&ag£$%$¤aa£bNSPTc*´µ895N~R^*PT024p4ŸPT*NSPT*P®P*.M*+,*³OPQ*NRNSPT

-0-VWXYIL.D.EC D.F!Z56=3>[5\4]5^7W_&`9&a-b.D.E

cC D.Fb!Z5;<56=3>d53>4e95;#96& f.g.D.F&h7i&bg!6=3>[5j4k5lm7'n- f.g.D.F&h7i&R0o& .f.b6p 6( tu95vL.D.Eg!w.<56=3>[

¦10r&ˆ6V‚ƒ§356¨©5ªz5‚4p6k…0$«t%958#95 010'()& 76,-9&

¬y[5›­0,-2&R0o

®&t+95$%&$234567;k…95&) &)$%&'()& 76,-356%0"m†96&R'(49]5k…95&)6U95 &

¯234567$n-'°90±9&k²3>56k²3>5;y>]ª5ln-$2345670³53:549]5k…95&)9#70h95

"+a-

¯234567$n-W_"#$%& ˆ6V"+5-00€R$2345670³53:549]5k…95&)‚ƒkn0 '(0oa95LC2

´µ¶·$%& & "™9&Žª5676&t™9$%& ¸.š6k…ª56( 95º«-$234567

012456789 

 "%&'()*+,95$ -/$-0123435678(+, 9:957;7'(<'=>(*+,95$-?9@A(+,95$-BCD(*+,95$-BE9@A(+,95$-?F/G/-012343569@H

 I012343562

JKLM"#$ $ OP9$Q $RHSTU+,7( =(W@HX

?YZ[3B\Z[3?2TU31]2^2S]_\6` 1]a126^a12S6]_Y6bc(8(*d7 &'(<'ec( Of2g2h$!ij+,7( =(7! OP9$Q 

$RHSX

BYZ[3?\Z[3B2TU31]2^2S]_\6m1]a126^a12S6]nY6o'p&q(<'+r&q(7;7( Of$st95$tu9 +,  9Hwx(*y&(zx=&({9 u "%&'()

*+,95$-'8=(<|c&q(8(78(*+,95$ (bc(8(&qcDA(7;7(zx>(<€ i67~H89$! 9i‚

ẹềc7|=<e(*D(&q+rHể` Eễ1t s!$ếij ể

bc(8(ặ{$ /ậHH)&()ệềc7|=<e(*D(&q+rAìỉ(Ä'+Å&q(Ä';Ä(ặ'ầ&q( k{$

O6Ú9³1t s!$ếij ´2

2±o|c&q(7;7( Of$.!9 /Û~Q&'+(<|+r95 9:95 ! !"5Hu F

 OG"#$"%&'()*+,95$- ~Q95 "#$ ấ$!"5Hu 9d$kĩ2 u~Q95

$!ijấ 9H%$ "#$ ấ$!"5Hu  Q$ 9Gc(8

íDA(c;&(&q+, ORHG9{6"#$k{$6Ú9 ~R&q(*+,95$- ~Q95$G"9Gti67~H899.$- u $H)&()24{6$ +Å&q(ò95 OG"#$$

ẫ6u )6 $‚F! $ đỏ&q(Ä'+Å&q(Ä';Ä(Cõ<(7R99:95 $ $ 9H{92Oà&(*+,$

~Q959567P9Ofẫ679Rij$sị 9G7@ỗố2

ộ67 P99{6 /l ặ'p&q({ờ(+, F 95!7   &'+&q(ởỡ $‚ ! ẫ6uOậ&ỉ(7;7(Ä'+Å&q(Ä';Ä(<|y&(ặ'p&q(ở‚~Q&q(+, /G$! i‚~Q95X

›œžŸÔžôơợœùžăâêôLMơ9{6$st95"#$"%&'()*+,95$ $ 9H{996# 9@A(+,95$-?9:95"#$ $‚ ỡ&'(&'+&q(<ỏ>(f !$Ú <+Å&q(ò95"G

"%&'() +,   $s$9ớ9$ "%&'()*+,95$-'8=(W=&(à6 ủ&q(78(7'ũ&(

“”e9 e6ˆ ^aa< /92 ]7C…9+X‹‰*

012456789 



 !"#$%#&'()%#*%"+95,6-. 2395.04/

5671239589.;99<%#&'()%#*%"+95,6-. 2395.0 8>(# ?@06:A B()

ltuvwxyz{y|uvyx}~€>(# ?5‚ƒ6„A ,6e4…0

D†‡5‚ƒ6„„ˆ‰Š

‹Œy{y

95c995"#()"#&^95.09/Hs5He@„D B()‘’(d6„ B()"#“ˆ‰4”() B()•–#p=7@67Z0„ B()‘gH‚—.˜7™2

4567I9:™9A74/ ja" ;6.i‚ƒs <GA

TghOi– —E˜P™95, ,JE>5`›-F.9,^RaUaO E™95,œ’

# š9.’E^-- "#$ !%&' E>5`›-F.9R,^RžRUŸ

ªA4´µLaghLi¶£ !¦·œFš -5?A) "#$ !%&' ]9E>F.9RaUaL

 - "#$ !%&' F.9R*+_5`RTUe "#¸A !¸•192

g:hi1 72I*l(8*mn(o

B123@1$%$67(8*+9pqI*L>D1Q@95 3 Ces()*+c*ptQu95$%$ 9H1

$>j_`ak?j_Bak @>j_Bak?j_`ak

@>_?jAa?_k C>_?j_? ak

>_?j_?_k m>llj_? ak?rja?bk?j_?bks

Rt2+I,95 !G #$6v I$ !G !p*w

$>ax _?a

@>Aj_?aky _

>j_Bak`by _Bja`bk

C>j_?akBja?bky _?ja?bk

2 (V676=AAWIXWAHSESYAZ1[0\AH]I^V67?48AAW_

‰Š‹Œ€‚ƒ…Ž‹Œ…€‚ƒ

Š‹Œ€…‚ƒ…Ž‹Œ…€…‚ƒ

2†‡(V67?489ˆ

‹ŒŒ‘€ƒ’…‚ƒ‚‘Ž€ƒ‘’…“ƒN4ISESF1[V67?48AYB_V`?a95n|67(^9;Ub

vwU )!'&!h5]C.99567292bc dO6 +!'76y

-fgzi C-g{i -|fg{i

E-ngpi -g}i~ng}i -|gfg€zi~ng€zii

2A>ghi‚nghi +0!:wƒ „!…†:!+ƒ[!\dey

‡ghijkhˆ‰k

Š8 dO6 +!'76y

-fg{iq~q‹ng{iq~q‡g{iŒ C-g{iqq‹ng{iq~q‡g{iŒ

-fgpiqŽq‹ngpiqŽq‡g{iŒ E-‹fgpiqqngpiŒqŽq‡gpi

-fgziq ‹ngziq q‡gziŒ -‹fgziqŽngziŒq q‡gzi

2A>f‚n‚‡ +0!:wƒ 

-Š8^Ih' fghinghi‡ghi'( )

C-Š8^Ih !'fghiŽ‹|nghi‡ghiŒ'( )

2bc4deghijkh‘€pho{’‰k2 C. dO6 +!'76y

-fg‰i C-gzi -fg{i

012456789 

 !"#$%&'()*95+

-/0123!4!56&789$:;$<&() =>???

@/0A,B C9DE95F = B C9AH95 9

/0JKB C9DE95F =FLB C9?E9M?9 AH95 9

,B C9A-E ?E9DE95F =>???

P/0JK!3!4!589$QDE95F = ?E9 ?E9M?9

S/0A,B C9T$<U95  ?E9M?9 LV(WX($YR

Ž20  !"#‘&’! D]2 W“9$%&‘2:(WX(”•6

 @–95 ]:(—-/0 KB˜ `ab96`f€bf €b

-/0„`a^_`cvh_`c @/ƒ‚`a^_`cuwh_`c

N/0‚`a^_`cxh_`c N/„`a·^_`cvh_`c¸x^_`c



JJY\+]^_ab95 Y7c>de=f>ghidj>ak>J@Bl+,-99567m9nJoH2

pqrstuvwxqyJoHJ

   "#$

%&'()*+,-.-/0123-4-56789:95;<;=>@6AB5?;C6D9E GHI 2J ;<;C6L9M;N C6OPQ,3RST-U/)*+,-2)*+,-PQ,3RS-,3L;<;V@+(-2WXY-/4-Z[X-+()-\]95V@+(-2W

45B_?`LEL;a+,-\b95;<;=> W62h<;=>@6iHj 2)k; ;<; l]2



mno p q ro s t ro

u0Q+,-R()*+,-/0)vR-/ 9?@VE `B95VFE7yg>9:T-2z;{?@E/0Q+,-2| 4-R~4-RĂR-P)k95E&€-u0Q+,-R()*+,-+Yd-/4-/ÂeE:;789:95 9?@VExe

E 4-/0‚;C6L9Ê2Ô-PY-+(+,-2y3-)k+,-2)k; A]? VFE> -+YQ-2Ԁ-Â6

†A_VFE E8;~LExe ˆ‰Lg?ÂE†Àˆ€-u0Q+,-/0)‹95 +,)k;A]?Lg?ÂE†ˆ2

Ž2d-(Ă3-+3@VME> J6E 4-(ÂE7‘;`F95`w?2 9N{? @9{1?VFEg|E&“”•Ả {?Â9•À—2 Ơ7E ƠE 8

•À—7LB “”•Ả2™+,-2)k;=>@6{1?Ê

ˆÃ›•À— “œ”•Ả

—2)k;5ž?_Exe ga-/0:24Â6—J695ƯVEˆ;NE g?ÂEÊ

ˆÃ›•ă“”•ẢÁâđê

Þòỏõỏóõọồổỗốỗố0?O78ˆHáA_Exe ;B9;~LExe ga-/0:—2 Ơ7

    

 !"!"#$

%& '() +,-).)/0 2345)/0 6789:;<:9=>?@A9B95CD9EF)3G%HI% )KLMNO2H() RMNO6H4)OES T6C4-ULV345W%C4XYZ[\]L^_%-2`O3%F)a

012456789 

0    2 "#$%&'()*'+,$-.$'/0$12 3495 56762 9:;<=>?9@

AkABCf}„

7BCkAf}~

JKLMNŠnN‹Œ‹ŒVN0A34 9:^X7YŽC7‘ ’\9“7{?XŽC7”• ’\9“7{?Y2i@a

đêSTfÁ95 “H- -91 ()*5/Á8ô952N)92/u126Â:Ă -q u4+,s-ẬÈẺ_ẼÉẺ_°Ẹ_ẼỀỂ2

Nô j=-.Q9-)12

ỄẾả#%ả·#ÌỈãÍỊ½¾Ư'%

/ê Òs- uEft192/4+Ẽáạ_ẼỀỂ6+12ơ q9h6-v9-Ả/,s- )u6+-io 1*9Ž™Ẫơ‘1r)2N)6/h-IuIơ2

/ê 4h6u )92/u°Ẹ_ẼỀỂ_

"#$%&'%

:*95 5/)u6+Ž™Ẫơ‘9h6u DTUVWDXYZDặF ÊDầRẩRẫDCYẳEấ/ 

-v9-Ả/,s‚DèUVWDBVYDVYfDẻi72

/ io u6+ẽEftCDV[ZDẶDEv954ắCDẨft959h612,s-:*95 uà ẽ

"#$%&'%0/â:q-v9-Ả/,s‚DEŒVDBVYD-ôu6+*ẽRDặ5-u6+4 ểễ.*95ẽ2 ,s- -q‹u-‰7À2N):éEF ÊD,s- jẢế>ẽ@ uVYfDèÊxệ

Ứê4h6ể-v9-Ả/867 u:)* RSÊDE5-

Ứê4h6ểễ›‚ÊDE5-‹