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"^ ` ? @*H  0޽h ? 3380___PPT10.Er@6 .1_Diseo predeterminado9  PH 4(  4r 4 S p!?'gR  ? ~ 4 XA޽h ?blackboard"@` 33___PPT10i.+rpFv+D=' = @B +   S(     c $A 4??PJS 8 4$D  0  0,n?, ( 2  0%G,$  0 cDonada la matriu A:  2f( ~  XA޽h ?blackboard"@` 334 , ___PPT10 ."r0+iD' = @B Dc' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* +8+0+ +  D< (      c $A 6?? 8 6$D 0  0v?<v,$  0 t&Volem demostrar la segent proposici:'(2'( 'H  0޽h ? 33t l ___PPT10L .$r ٸp+|AID' = @B D' = @BA?%,( < +O%,( < +D' =%(DS' =%(D' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<* %(D'  =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D'  =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* D'' =%(D' =%(Dw' =4@BBB B%()))D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* +8+0+ ? + $9(  $ $ 0?   3Comprovem que la proposici es compleix per a n = 2>4(2.((( 4H $ 0޽h ? 33___PPT10i.%rЕt+D=' = @B + (q(  ( ( c $A 8??Tp 8 8$D  0 ( 0 ?",$  0 U En efecte,  2 (  ( c $A <?? 8 <$D  0 ( c $A >??-8 >$D  0 ( c $A @??p&8 @$D 0H ( 0޽h ? 33___PPT10.%r+4D,' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D'  =-s6Bwipe(left)*<3<*(D' =%(D' =%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-s6Bwipe(left)*<3<*(D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-s6Bwipe(left)*<3<*(D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-m6Bbox(in)*<3<*(D+' =%(D' =%(D{' =4@BBB B%()))D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-6B+checkerboard(across)*<3<*(+8+0+(? +F H@0(  0 0 0? n,$  0 qAra hem de demostrar que: 2({ 0 0?_,$ 0 1Si prenem la proposici per al cas n com a certa,2(2   27 0 0?S  ,$ 0 %Tamb es verifica per al cas segent:&(2&> 0 08? M ,$  0 =n + 1 22H 0 0޽h ? 33___PPT10~.)r7+(12Dr ' = @B D- ' = @BA?%,( < +O%,( < +D ' =%(D' =%(Dp' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-o6Bwipe(up)*<3<*0D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-6B'blinds(horizontal)*<3<*0D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-6B'blinds(horizontal)*<3<*0D$' =%(D' =%(Dt' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-s6Bwipe(down)*<3<*0++0+0? ++0+0? ++0+0? ++0+0? +  0 8(  8 8 c $A B??' (8 B$D  0l a   8 ,$D  0@ Jm m  8Jm mTB 8 c $DJJmZB  8 s *DJmm m  8 0?a  0Per hiptesi d inducci: 2$   8 c $A D?? s8 D$D  0 8 c $A H??c 8 H$D 0 8 0(?C'Y] ,$  0 ?I, segons la proposici que volem provar, aix hauria de donar:@ 2@ @H 8 0޽h ? 33LD___PPT10$.,r3+V/CD' = @B D{' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =-s6Bwipe(left)*<3<* 8D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =-s6Bwipe(left)*<3<* 8D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8D' =%(D' =%(D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-u6Bdiamond(in)*<3<*8+8+0+8? +  `@-(  @ @ 0Ҫ"*,$  0 aVegem si es compleix: 2, H @ 0޽h ? 33 ___PPT10.6rPCu+׸D' = @B DD' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*@D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*@+8+0+@ +  \T@<(  < < c $A L?? 8 L$D  0 < c $A J?? 8 J$D  0 < c $A N??, 8 N$D  0H < 0޽h ? 33'  ___PPT10 .6rd+ak]D ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-s6Bwipe(left)*<3<*<D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-s6Bwipe(left)*<3<*<D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-s6Bwipe(left)*<3<*<+  *"D(  D D 0?z n,$  0 Z Certament, 2 (  D c $A P??"&s 8 P$D  0H D 0޽h ? 33  ___PPT10m .6r +oD ' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-s6Bwipe(left)*<3<*DD' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-s6Bwipe(left)*<3<*DD' =%(D' =%(D`' =4@BBBB%()))D' =0l9 CCBB*<3<*D+8+0+D? +R H#(  Hb H 0d?,$  0 4Aix doncs, si la proposici es compleix per a n = 25(25(Z   H <? ,$  0 5i( H 0? ' ,$  0 2Es compleix el cas n + 1, suposant cert el cas n: X3(2(((((bH H 0޽h ? 33g _ ___PPT10? .7rB5C+/"zD3 ' = @B D ' = @BA?%,( < +O%,( < +D8' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bwipe(up)*<3<*HD@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bwipe(up)*<3<*HD' =%(D' =%(D=' =A@BBBB0B%(D' =0l9 CCBB*<3<*HD' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bwipe(up)*<3<*H++0+H? ++0+H? ++0+H? ++0+H? +c yL(  Lq L 0Dz t ,$  0 ?Podem afirmar que la proposici que volem demostrar s certa  @82@(Z  ` L c $A z?? j   zH L 0޽h ? 33___PPT10b.7r+_,D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-o6Bwipe(up)*<3<*L+8+0+L +"xXoG3k;1 5KTAphY"iDL+qLjb/-R*ZS/TZ **d vg5y}fo =BJl} @+W*RT\(: i@RXgPo ixΜlCaYȲ5|>7rxx:F.iSMɴ8#يeuaZ;z*3ڽf`& uz#d =!xǶeQP[sI>p}}3P;|e$5i5#d^v*򹻡6X#E\qӉ A7 Єd ͯ&5+fN%0mvcكe.p-$Ϥ ?o]v5E]Gnb70P p~s^P}jGWTGo+L `rlhF_GWh|AxMsG SF!t~"g?4fY{Uz2 LfFLEU\&{A}i6S Ǵ{ 3AI/ Ɛ ǩZKb%g &&bzZ0qQ#)`?ʪ"a7:W$a{g/:'R'ۄa aԠw/|Z#}_ǐ 1<4@-(E A$A[mr^CׅʔA/bCEihVdEC2c_+{_([O{ѺQa1+Y40 ~^RКjܺ&z4dwcbC~c7]Ҫk=_^b!!QGM{f?N)-˰wHôlHRK9wz+W:PbTWs8ìԽ{A`DD:exmD?fވ aPzyuscӏ5C=eFYX#Vn#;h㼓A?;5/nŊ1Xy>H %ؔoۼ%'NW$xXoh[U?&m;unoՍ9iaYe4$kaԁ *A˦ ɠ2eWtAlx}&/־,lpw9+SJ C[4 (Bv]aUoN\6<$k[ϯ$wJzF!VM+3-}ώN+rLBwsH9 OZގ3G 8p^^B>HiG!W诘Xn#έ0縠|{pB/ɎNbu&qٮ}ku7Ai 2rN6/q31c0~O [gG|RML1 б݅܁0#Ȼ@eѠ!zhl2I a 4®`q=M[]_p]1 >zDDpxr*f%S8 (}Ӯp> s vfEqS3 fHo`'/r [s .E>nAޠ^T eB;W5~EdK]yZkxz*r'լL+҅y).Kjj?IJ U&scslgGxf̏w "?`?\72p*V*xYMlE~3k;b;l#@KS'jT  qѸخJH%BH.\CoRP{HV)H918؎>{fۙ}{3?~xc0۠j 2]/[- T`*XTrɀ 59) d_6߄c]gSlr`"Ua 6m60?%| i]Tr}c8HOT.8j_.L,o4/UCO>XS)32U}H$qq|g͊6X4D^>w\WA%%[??!S_鉿]  .0?q2>ث__~Lb: BaL+NaCMq$$QO@r2&%535HeH)i4< <:{5{vrVנvHD OLEGHZdsX8^e<@`b2H ^gCG]0| (?}:9{.Ӂp~Z+Ø y. s *%I _Qm*Ty]~l@mZQ)Q߫_}~:Yە{s 2n4>S?{3N&ܪE{~/8^CRDxN:dB>'eMKL)~9džZڹ8ÍF@(`:&C0-r= Q/m)P.2yWŊ7`Rgfѝz n#rFޗD?0M}y5Jx_ @WNAGdZ4^~3 W8JTq̒J D2f[,t:lTx}%VTY|d}y},!sEjl}:8u.=uu{eϟ,oZ70XavѼƍ\:ѝW_3Gݬ(-wj*ђQUQըjp⟴7mݞ珒7H*h3c=83OܮMv~!>4yZ<:FɟxYo5xwwX[뿭j/ 2N"xXMlG~3k;xb;4.UZ**I!i8TiWOps.UTUqK9S$~^Pe`xcՎc(6eΛ7?o=/}CPE\:aՕ2U)P4)|rI,30[ ui;8ϜAYRCÙkLEt ƚlIȶFՒuH Dq1܇$ØvYilľ9τ`&1+ 1\bJ:jzd*?aJa6 "x6^fs}^ t?y@zk7[ulSۀrȽ;_Aމտ!Aʿ B|^̿҇hF\UȾg7ưO}d3]ƛƀ@pA:D-%1tIb4vXu\pˋy@t2/; .iFFq NV0'钘@Tp,ad1#M$\z%_@ Mk} |{Ws  ,2/EOg=&G;n񿸴Yl9V}{Q{hzz&L5!s'r`dr4nv|xcy;Epciǒx`4t816wV̯L&NdbFw5\&hi>}nd_h~mۼ!(=Ź|a*ȑY3#(FF"zB^9Ǖyf*xI8;!) 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