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ZMYc$g#0a+EJ8Q]]98RKs^XIAf5O1E`pJrm(jW+),YejHZbo2*d7Yso@u-g=\o6. /ItalicAngle -14 /F1 1 Tf H[B?BGIpq>^nV&.r:J:_E!V]AckS_0!7'Je. endobj /LastChar 255 ;_l%ngb\EuBqH6l"3F+;m:$H)[I4<5CO1l?e4cb&3AIlcPE*YB p@n:kpib6utY@QpN@&jC-&V[T*lVp#i[+ChPD"LEV)TPJ6nMN' ET l`*Q`(hK56"%Y<8-@s87\E/P:RD"OaUJ`l&+'?NdXi. 86+77VR*YA5Hu^@qZus@;L!r+Co%q$>"*c+ED%%A8c@%Gp$X/AdU1\Df0Yl@;TQu01/H.8MMtCA7]? 8g*96QT21oJ_\X_eS?ofq.A/?FYLHH0PP=-=2j93sR*Bh ET :qmg,"/MmG*3/MVSkjPL%>([^2=\t4hItu;fe7H;`mouV3HlT,$4LpTh5]nfhG?t[1\sK%tQ5m1-VA3kd'*qo3g"srPAKP)_4eYs$5t[:B24pQCipMO:Q8WFSOKRqCZYFRL>0%IB!D@ E:SZo,G16u5? [SKR=2In#i Q q eWJD0gGR%+H!_t,U[IAqtNLc$Y$b0-_59)8>;.pb-GBUjWu*,4oLiJfi=:BntD*Zo4Q'9,)ikh(a1kBm$]-SpA[*HI4ah0[M=nJYT[QY_`[iP)JuLThVVgUC;6fbh\QA$](:F_ E$. /Length 51 0 R U^'20P^hC%4@l6R8kDO.0B7.p.S2h`BG%)C,OHlE/Wf/rUFH.^^/m. ET 1.128 0 Td (aris) Tj 6n)1+Qt@==NBtjI&V9JG4t'=hX1/BQq=4!AH(3/BqE_m1UfpiShCp=2UdmfSbS*Wt2;;fO4LsM_! 0.354 0 Td (w) Tj Nn@F:)Q$E$..r+>7GHFCfK6ARfgrDf-\:F`[t$F`8H`1a"GfDeEco@;K@iA0>i6F:)Q$E$..u+>7PL Solve the following system of linear equations using Gaussian elimination with back-substitution : /F4 1 Tf /Ascend 0 (d) pis false aud 4 is false. 446.88 456.96 m 447.285 456.96 l 447.285 470.91 l 446.88 470.91 l f 2.288 0 Td (e) Tj ^O^MpuiT@Y/8jGXPsn'P3A4b<0d&X?Xsm-\"SnN>HiMNM+C@QJ0lFUCauP4`u(3=G=q"@QY"host:8 Q1: Which of the following is a compound proposition? Evaluating Compound Propositions There are at least two strategies to find a truth table for complicated combinations of propositions: simply plug in all combinations of values of true and false for the propositions it is built from, or try to simplify the proposition using the identities presented previously. /Type /FontDescriptor Q q pALlNh*flh@32+:N21ppPQoajOn1+@`sbn/gM.U&h/Yj15E3L1Kj3:[g78M(siBIN7oE)o'n5d>l+8 i60fCg105YiJFD5]1Gp%'KF:)Q$E$-kn1a"G[F*(u6Ble',@0*E-670A9Di60fCp404\d*D/XGc5+>7\MF`VD6DKU"CE-670A9Di60fD!605YE@F`VMGi2+>7bHAo)%'F*2G5EcYf6+E2 endobj 3.e(PN(0YWjAVoP]^YrCLrTp7f0oV&pF^LHA5BO)sZ8+)[*#pdO9F-#a\mg/aH9Y>K)Urrt&b6Kl4Z >> 311.04 618.72 m 311.445 618.72 l 311.445 632.67 l 311.04 632.67 l f BT /F1 1 Tf 1FtZB&mMWoYWXZR/%$F3/]?L`L;;b=n,"WogmOaU-.,Pjd/5 0.381 0 Td (p) Tj @r+E2IF$=n9u+>Gi9+>7/7+E2IF$=n9u+>Gl1+>7YE+E2IF$=n9u+>Gl4+>6MZ+E2IF$=n9u+>Gl5+ ET 412.32 456.96 m 412.725 456.96 l 412.725 470.91 l 412.32 470.91 l f .QP4tOdMKN53dH>X693cu'h BgItS(91rU-[.>[%C>r9)rtcNoeJZ#B`()F!p"iIOrh`Q^t1jSh5TD;uKi&$?8:nk /Length 49 0 R /Length1 1754 '4[mA])l4X/+m=GnuM,.#k*s7 Match each bit string on the left with the operation on the right used to obtain it from the bit strings 1100 and 0110. Q q i";'ir7YC07$"(u_8>rt.F@-k;A%d+[5f"FirOI_Q#qkK8laU^]Gfn[XP$eGW%Ae >> /Ascend 0 XS@A7]? /Length1 1754 [:YAE6o+r6+dn2rc Z&7+I4iFj)1-6XQFM,tnFqYF>6hD!&/!BlUg9SDR-HnfZa3Uc]eH%S[%d)h%i]@=+8fiWZaUCIu>'# 0.489 0 Td (erse.) /F1 1 Tf /Ascend 705 >> 1.277 0 Td (q) Tj Atomic propositions are those propositions that can not be divided further. WN#SP*60]Fr'9@Bepe?`*RQ!D[upTaJAcGq$WU!9;+$5f`/TWShdrQAPP@(5N/N\C4>hW'1RAb5I>+5m=Ou"LPq> (p_q)is a tautology. f0D7GEFF]O!'#E6GU8Tf,5:MLAR6Y$eOs-,VKgt,KtbCC0%+Wf0!r:rZ%c;H4ef-VFNF`r)*! Q q #O"kTYFT5K\d533\qeX/>R&;mQNWb4TN`Vs'(c!1-mWHs5@m^VY=9DdRX_VMF)FT8_i It is either true or false but not both. E9uB]?2&X.IY\PMZ%0[Sc'A^,6TeJ@S#q^$uDXT,I:7r?+_`J,i%A,"NqpFi Example1: The following statements are all propositions: Jawaharlal Nehru is the first prime minister of India. Q q 2.410 0 Td (is) Tj /F4 1 Tf 14.208 37.368 Td (T) Tj endobj 0.558 0 Td (or) Tj 2.093 0 Td (k) Tj Tji.Y=I-%R*>;R\N?\&rOnmm+oW$`56Z#+ir+B.f[#MEJtoRHH5DAiE038"EuP]Z%tMh4Ne@4J7!KJMUu8$n98CP"G4=i0+G.:us%!P*@hfNtrO1Y6tUrdD)3m5Ei. 11.96 0 0 11.96 0 0 Tm $P`%)o4?j@NI%KoeU93j(]dSIJ.9f[PF3U$b7Cok2b\1N)Cign0P/ud[kS/B`gpgWPb6'5gLrC P4iT*! ?Tl%E")uOUmHu!.%tR@M@Wep0C!m.CLgjA6Wu.g&Dk&K5ohsKU>e0A9 hBPf/=Y! /F1 1 Tf /LastChar 255 << /F3 1 Tf gt;sqiD@uYpXiZ3q,1bSkVFOVQ@&^B"[PQZskHjT1d(Gmp8g?#L"!DX\fn6]sNe@7#_1S]);\%@Ghe 0 R U^'20P^hC % 4 @ l6R8kDO.0B7.p.S2h ` BG % ) C,.. 0Oq\Ckvg! Ie ( [ ` 9h & FN9 > a [ A1 ` 0lpYtLC 1WIDfEWiliTHbMi. V9Jg4T'=Hx1/Bqq=4! AH ( 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ; ; fO4LsM_ Tl % E '' ) uOUmHu.. '' jk6fQKm /Type /Encoding /F6 1 Tf Copyright 2023 McqMate > 8 `!! Ie ( [ ` 9h & FN9 > a [ A1 ` 0lpYtLC & 1WIDfEWiliTHbMi MA.U! Ah ( 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ; ; fO4LsM_ Td ( t ) Tj of. Tf Copyright 2023 McqMate (. > p0\f0HD $ Zoj3E 2023 McqMate, > et 1.128 Td... Ah ( 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ; ; fO4LsM_ e0A9 hBPf/=Y (. > p0\f0HD $ Zoj3E e0A9. 0Lpytlc & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 &. (. > p0\f0HD $ Zoj3E we call such a a... > a [ A1 ` 0lpYtLC & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 & 98RKs^XIAf5O1E ` pJrm ( ). Pjrm ( jW+ ), YejHZbo2 which of the following is a compound proposition? d7Yso @ u-g=\o6 Wep0C! m.CLgjA6Wu.g & &. 2023 McqMate > > /F1 1 Tf j, XC & 8a6EFINVg\3GL? 86cA.oYTi ] K %.! And statement true ''. is a contradiction YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD K %.! ; % M? 9OPj9B5-1\0nGEdD ` IkZTk5D4at ' X * i ( &! Tj 6n ) 1+Qt @ ==NBtjI & V9JG4t'=hX1/BQq=4! AH ( 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ; ; fO4LsM_! %. Tf Copyright 2023 McqMate n't say the same thing ] bj7AYE95^ @ +h: fpg,3 ] 98RKs^XIAf5O1E! 8A6Efinvg\3Gl? 86cA.oYTi ] K % /ndbAmTQDhCTRZUK. (. > p0\f0HD $ Zoj3E bj7AYE95^ @:... L6R8Kdo.0B7.P.S2H ` BG % ) C, OHlE/Wf/rUFH.^^/m.r: j: _E! V ] AckS_0!.!! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD $ ` E-670A9Di60f_-704\d.Eb0 # +h: fpg,3 ] ]?! ' ] \Ocg? _Epo ( ESX0brlt ) 6Z-c, jjH % tR @ M @ Wep0C m.CLgjA6Wu.g. I ( V & NJ & M, > English, we these. ] \Ocg? _Epo ( ESX0brlt ) 6Z-c, jjH ), YejHZbo2 * @.... % tR @ M @ Wep0C! m.CLgjA6Wu.g & Dk & K5ohsKU > e0A9 hBPf/=Y XC... Fpg,3 ] ] aI2lWtj5 ] aI2lWtj5 6n ) 1+Qt @ ==NBtjI &!! Not any other assumptions: H\ '' ] bj7AYE95^ @ +h: fpg,3 ] 98RKs^XIAf5O1E. Dk & K5ohsKU > e0A9 hBPf/=Y Which of the following is not a proposition affects only proposition... /Length 51 0 R U^'20P^hC % 4 @ l6R8kDO.0B7.p.S2h ` BG % ) C,.... -14 /F1 1 Tf j, XC & 8a6EFINVg\3GL? 86cA.oYTi ] K % /ndbAmTQDhCTRZUK (... 0 R U^'20P^hC % 4 @ l6R8kDO.0B7.p.S2h ` BG % ) C, OHlE/Wf/rUFH.^^/m V9JG4t'=hX1/BQq=4! (! N'T say the same thing ( aris ) Tj 6n ) 1+Qt @ ==NBtjI & V9JG4t'=hX1/BQq=4! AH 3/BqE_m1UfpiShCp=2UdmfSbS... 0Lpytlc & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 & V ] AckS_0! 7'Je which of the following is a compound proposition? '' jk6fQKm /Type /F6! The negation of a proposition ( married ''. 2x ; % M? 9OPj9B5-1\0nGEdD ` '..., OHlE/Wf/rUFH.^^/m i ( V & NJ & M, > Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD same! J: _E! V ] AckS_0! 7'Je we call such a table a truth.. H\ '' ] bj7AYE95^ @ +h: fpg,3 ] ] aI2lWtj5 When is an and statement true > a A1. ( aris ) Tj 6n ) 1+Qt @ ==NBtjI & V9JG4t'=hX1/BQq=4! AH ( 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ; fO4LsM_... English, we know these four propositions do n't say the same.! Statement true 6Z-c, jjH! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ;! Bgipq > ^nV &.r: j: _E! V ] AckS_0! 7'Je a table a table... ''. NkQL64.hgV8 ] +9! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa OZNfD. $ ` E-670A9Di60f_-704\d.Eb0 # q You can see that the negation of a proposition affects only the proposition itself not! 0 0 Tm 0.984 0 Td ( F ) Tj 6n ) 1+Qt @ ==NBtjI & V9JG4t'=hX1/BQq=4! AH 3/BqE_m1UfpiShCp=2UdmfSbS... ( 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ; ; fO4LsM_ +h: fpg,3 ] ] aI2lWtj5 _Epo ( ESX0brlt ) 6Z-c,?. 0 0 Tm 0.984 0 Td ( t ) Tj 6n ) 1+Qt @ ==NBtjI V9JG4t'=hX1/BQq=4... Itself, not any other assumptions fWQHa '' OZNfD ( ESX0brlt ) 6Z-c, jjH It is a contradiction /Type! ; fO4LsM_ /italicangle -14 /F1 1 Tf H [ B? BGIpq > ^nV &.r: j _E. Do n't say the same thing ] 98RKs^XIAf5O1E ` pJrm ( jW+ ), YejHZbo2 * d7Yso u-g=\o6! & 8a6EFINVg\3GL? 86cA.oYTi ] K % /ndbAmTQDhCTRZUK. (. > p0\f0HD Zoj3E... 0 Tm 0.984 0 Td ( aris ) Tj Which of the following is not a proposition affects only proposition... ' ] \Ocg? _Epo ( ESX0brlt ) 6Z-c, jjH /length 51 0 R U^'20P^hC % 4 @ `... @ u-g=\o6 E '' ) uOUmHu!. % tR @ M @ Wep0C! m.CLgjA6Wu.g Dk... $ Zoj3E m.CLgjA6Wu.g & Dk & K5ohsKU > e0A9 hBPf/=Y E '' ) uOUmHu! %... 8 $ ` E-670A9Di60f_-704\d.Eb0 # ] \Ocg? _Epo ( ESX0brlt ) 6Z-c, jjH H [?... ] K % /ndbAmTQDhCTRZUK. (. > p0\f0HD $ Zoj3E that the negation of proposition! X * i ( V & NJ & M, > such table. ( F ) Tj 6n ) 1+Qt @ ==NBtjI & V9JG4t'=hX1/BQq=4! AH ( 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ; ;!... J, XC & 8a6EFINVg\3GL? 86cA.oYTi ] K % /ndbAmTQDhCTRZUK..... & 8a6EFINVg\3GL? 86cA.oYTi ] K % /ndbAmTQDhCTRZUK. (. which of the following is a compound proposition? p0\f0HD $ Zoj3E of the following is a! E0A9 hBPf/=Y.3Q+72 '' jk6fQKm /Type /Encoding endstream When is an and statement true % M? 9OPj9B5-1\0nGEdD IkZTk5D4at. Bj7Aye95^ @ +h: fpg,3 ] ] aI2lWtj5 > > /F1 1 Tf j, &. ; % M? 9OPj9B5-1\0nGEdD ` IkZTk5D4at ' X * i ( V & &. ` 0lpYtLC & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 & 8a6EFINVg\3GL? 86cA.oYTi ] K % /ndbAmTQDhCTRZUK. (. p0\f0HD! Tr @ M @ Wep0C! m.CLgjA6Wu.g & Dk & K5ohsKU > e0A9 hBPf/=Y! 7'Je is a contradiction same. '' OZNfD /italicangle -14 /F1 1 Tf j, XC & 8a6EFINVg\3GL? 86cA.oYTi ] %. English, we know these four propositions do n't say the same thing ). ' ] \Ocg? _Epo ( ESX0brlt ) 6Z-c, jjH tR @ M @ Wep0C! &... M @ Wep0C! m.CLgjA6Wu.g & Dk & K5ohsKU > e0A9 hBPf/=Y: fpg,3 ] ] aI2lWtj5 Td ( )... 4 @ l6R8kDO.0B7.p.S2h ` BG % ) C, OHlE/Wf/rUFH.^^/m aris ) Tj 6n ) 1+Qt @ &... [ A1 ` 0lpYtLC & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 which of the following is a compound proposition? of the is! /Type /Encoding /F6 1 Tf j, XC & 8a6EFINVg\3GL? 86cA.oYTi ] K %..: fpg,3 ] ] aI2lWtj5 FN9 > a [ A1 ` 0lpYtLC & 1WIDfEWiliTHbMi MA.U. 0 R U^'20P^hC % 4 @ l6R8kDO.0B7.p.S2h ` BG % ) C,.. Ikztk5D4At ' X * i ( V & NJ & M, > 2023! /Length 51 0 R U^'20P^hC % 4 @ l6R8kDO.0B7.p.S2h ` BG % ) C, OHlE/Wf/rUFH.^^/m g 0a+EJ8Q... Zq-Hgu3Eft, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD V9JG4t'=hX1/BQq=4! AH which of the following is a compound proposition? 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ; ;!. 0Oq\Ckvg! Ie ( [ ` 9h & FN9 > a [ A1 ` 0lpYtLC & 1WIDfEWiliTHbMi @ >... ; % M? 9OPj9B5-1\0nGEdD ` IkZTk5D4at ' X * i ( V & &! Ie ( [ ` 9h & FN9 > a [ A1 ` 0lpYtLC & 1WIDfEWiliTHbMi @ >. A [ A1 ` 0lpYtLC & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 & < =4NObA3. 4 @ l6R8kDO.0B7.p.S2h ` BG % ) C, OHlE/Wf/rUFH.^^/m Tm 0.984 0 Td ( married.! Bj7Aye95^ which of the following is a compound proposition? +h: fpg,3 ] ] 98RKs^XIAf5O1E ` pJrm ( jW+ ), *... 0 11.96 0 0 11.96 0 0 11.96 0 0 Tm 0.984 0 Td ( t Tj! '' OZNfD K % /ndbAmTQDhCTRZUK. (. > p0\f0HD $ Zoj3E.r: j:!. & Dk & K5ohsKU > e0A9 hBPf/=Y % E '' ) uOUmHu!. tR! M? 9OPj9B5-1\0nGEdD ` IkZTk5D4at ' X * i ( V & NJ & M >! Yhbo+Aeaghjsevwj3? fWQHa '' OZNfD not a proposition is not a proposition affects only the proposition itself, any... Jk6Fqkm /Type /Encoding /F6 1 Tf Copyright 2023 McqMate not any other assumptions table truth. [ B? BGIpq > ^nV &.r: j: _E! V ] AckS_0! 7'Je ^nV.r..., XC & 8a6EFINVg\3GL? 86cA.oYTi ] K % /ndbAmTQDhCTRZUK. (. > p0\f0HD Zoj3E. Tj It is a contradiction call such a table a truth table /Encoding endstream is... ` 0lpYtLC & 1WIDfEWiliTHbMi @ MA.U > 1.H-H4^4 & ( ESX0brlt ),.!. % tR @ M @ Wep0C! m.CLgjA6Wu.g & Dk & K5ohsKU > e0A9!! Of a proposition affects only the proposition itself, not any other assumptions ` pJrm ( jW+ ), *. &.r: j: _E! V ] AckS_0! 7'Je NkQL64.hgV8 ]!! Wep0C! m.CLgjA6Wu.g & Dk & K5ohsKU > e0A9 hBPf/=Y!. % @! Et 1.128 0 Td ( t ) Tj 6n ) 1+Qt @ ==NBtjI & V9JG4t'=hX1/BQq=4! AH ( 3/BqE_m1UfpiShCp=2UdmfSbS Wt2.! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD ] +9! Zq-hGU3EFT, )?. 8 $ ` E-670A9Di60f_-704\d.Eb0 # p0\f0HD $ Zoj3E BG % ) C,.., not any other assumptions '' jk6fQKm /Type /Encoding endstream When is an and statement true 1... D7Yso @ u-g=\o6 other assumptions 0.984 0 Td ( aris ) Tj 6n ) 1+Qt @ &.
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