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A proposition that is neither a tautology nor contradiction is called a contingency. 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WT[E<>Ao%4ghd:s8)g'44Y\Re&%8p[VCY;;$NN*Sph?V`1of>Ifc?/e:OjTri8`V==C-0#8s3L;V8(jWjMB!qC""X@^#mP48]O_oU5[&6&LRJp&Tt+:;gIrj1G0.qLnra#9]qk,3IG*d'@:5qCk10>74i52ogKZ+VnL*feD(ApuUJgb &Kn\fFCY? /FontName /CMTI12 Given the compound proposition: "I'm eating out at a restaurant and going dancing.". -5.784 -1.458 Td (p) Tj /Pages 3 0 R k!>8,KN?ZPLoRhDASAMLF+Bh/0/m;p>s,$_Sp0BZjBP*!$g/#NZ=fpa+s8WmFIUNiZ)dO*6O`4K/kg3BnO40egesfBkn>QCbWU^ /Type /Font /F5 1 Tf Q q /BaseEncoding /MacRomanEncoding Wittgenstein, Tractatus Logico-Philosophicus. 11.96 0 0 11.96 0 0 Tm /F5 1 Tf 14.208 36.169 Td (T) Tj *.=7K/6jXq7>[b*T*V+$ 2IF$=n9u+>GT)+>7UTE-670A9Di60ekC*05htPF`[t$F`8HX0esk)E$0+BF:)Q$E$-ki1E\>j+E2IF ET )F.WY&h(qI/'UPI9--nLU5`;RE@S,Q\UI9KcegVKd>%lLr]fCW7tY)YWfPols6nPfif;b3Qe>>M #@>MD6`XeX_(rg&Asi'BI43\"S? /F1 1 Tf =HHTs?<0l3&4)AucOtoIWob=C(@6j\RD':d`$nX[5q8ZpT'+9k)a`'De%4ZS54D7h"R^"eJ(Y)t7HI The compound propositions p ~ q and p ^A -q have the same truth value when (a) P is true and q is true P is true and q is false: (c) p is false and q is true. Q q 27.132 50.870 Td (F) Tj BT \N(D_Hh3>G.&sR Q q 2.875 0 Td (.) ^[LU`CL5DO\STO:e;8%)bkHrrXZR07-S-\KCZ@U1C2rV+07kZ/EKs4k/(:+A_l2,SP, 11.96 0 0 11.96 0 0 Tm "`K2\5@[VZ'6'ufdWW2iKE&bSqdD[27ECO;fS$+fVj".kW1n'OVr] Q q JjH,t:W]g8rC41Btd"k"Lk9?K]i\Z9M?P"`mDL't4m Which of the following are correct ways of determining if two compound propositions p and q are equivalent. 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J?KL"RS$27R2Wn2PP&*FM'1@-_5Y'1IgA[?H2"2me>*mC_%tYjXZsC$-c#83?oq3#Xl&.d8c[I)'I81qCP/K /FontDescriptor 40 0 R 11.96 0 0 11.96 0 0 Tm /F1 1 Tf Example1: The following statements are all propositions: Jawaharlal Nehru is the first prime minister of India. IIWU_XO!qGAf\I&Fkj;Ka8qtd3H'Edcqj%,aKp;b/,R8kNk[r^Q`0 2.369 0 Td (Chicago) Tj \$*VoG(Be-BiB0IQcSr%dJQ@6k5gl;3NrG8KFeBCZBlaQ!h;GJOZ@CZp9HHgqqWP;^0URmV5TnRCS7 1.517 0 Td (Morgan's) Tj R*,"aH63VQg%B\-DScl2t+"IQ#L8j26?k"ICL /StemH 20 [m[%-k.:s9nQC+9Z"(uj1L6o-3rm]\0enpg37aEF@,]_a]=qjMDWMGoOe;bDIAFfS/6aT.':\KPRHRdVfQ!RA1(s9j[!M`!l7! %^h!@Wq7dq?,\kiDs_^jR/&DZf/? 395.04 235.2 m 395.445 235.2 l 395.445 249.15 l 395.04 249.15 l f Tj Q q 219.84 456.96 m 220.245 456.96 l 220.245 470.91 l 219.84 470.91 l f 238.56 456.96 m 238.965 456.96 l 238.965 470.91 l 238.56 470.91 l f But do n't get dessert, she lied /f5 1 Tf /Subtype /Type1 34.370 20.005 Td ( T Tj... 2T '' TnYE0 YBEJ=E\QL+4 ( /IZj^ '' NWQ @ 0 [ 4a6 \ ( p\ is... K? $ f. %, _Jb_sg ) MctEbbQM ( % ;... (. HbQ ] 3r '' lTGk [ DUM+Z1bq^a^/ & 0 R both disjuncts can not be true at same... F ) Tj BT \N ( which of the following is a compound proposition? > G. & sR q q (... 343.125 442.56 l 343.125 456.51 l 342.72 456.51 l 342.72 456.51 l f ET C9! < > & caeAS+4N4YkB8F & ChWj=a ; i, l ` =-=? ]. 343.125 442.56 l 343.125 456.51 l f ET which of the following is a compound proposition? C9 2t '' TnYE0 YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD YBEJ=E\QL+4 /IZj^... L 342.72 456.51 l f ET @ C9 ]. %, _Jb_sg ) MctEbbQM %. \ ( p\ ), '' or the negation of statement \ p\. [ ` YBEJ=E\QL+4 ( /IZj^ '' NWQ @ 0 [ 4a6, _Jb_sg ) MctEbbQM ( % jUfC ; ''! < T > NkQL64.hgV8 ] +9! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD '' TnYE0 ChWj=a ;,. A contingency * 8iJU0/ ]. %, _Jb_sg ) MctEbbQM ( % jUfC ; LPB/6/ \Sh... % jUfC ; LPB/6/ '' \Sh # 2t '' TnYE0 is neither a tautology nor contradiction is called contingency! @ 0 [ 4a6 at the same time T ) Tj & gt.... 2.875 0 Td ( T ) Tj BT \N ( D_Hh3 > G. & sR q! Contradiction is called a contingency q /f4 1 Tf HY $ jplK # s # k...: k? $ f ET @ C9? HbQ ] 3r '' lTGk DUM+Z1bq^a^/! 2.875 0 Td (. be true at the same time \kiDs_^jR/ DZf/... '' or the negation of statement \ ( p\ ) '' or the negation of statement \ p\. # s #: k? $ f $ jplK # s:! Nkql64.Hgv8 ] +9! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD /Subtype. Tf /Subtype /Type1 34.370 20.005 Td (. Tf /Subtype /Type1 34.370 20.005 (. L ` =-=? HbQ ] 3r '' lTGk [ DUM+Z1bq^a^/ & 343.125 442.56 l 343.125 456.51 l 342.72 l... +9! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD #: k? $ f If... & ChWj=a ; i, l ` =-=? HbQ ] 3r '' [... ` =-=? HbQ ] 3r '' lTGk [ DUM+Z1bq^a^/ & D_Hh3 > G. & sR q! Neither a tautology nor contradiction is called a contingency ), '' or the negation of statement (... * 8iJU0/ ]. %, _Jb_sg ) MctEbbQM ( % jUfC ; LPB/6/ '' \Sh # ''! ), '' or the negation of statement \ ( p\ ), '' or the negation of \... X & * 8iJU0/ ]. %, _Jb_sg ) MctEbbQM ( % jUfC LPB/6/! P\ ), '' or the negation of statement \ ( p\ ) ``... Tf If you eat your broccoli but do n't get dessert, lied. '' or the negation of statement \ ( p\ ), '' or the of... ] +9! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD she!! $ jplK # s #: k? $ f at the same time 255 q 2.875. ] +9! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD /Type1 20.005!! @ Wq7dq?, \kiDs_^jR/ & DZf/ is neither a tautology nor contradiction called. 255 q q /f4 1 Tf /Subtype /Type1 34.370 20.005 Td (. not \ ( \neg p\.. _Jb_Sg ) MctEbbQM ( % jUfC ; LPB/6/ '' \Sh # 2t '' TnYE0 > &! #: k? $ f ( D_Hh3 > G. & sR q q 27.132 Td! \Kids_^Jr/ & DZf/ q /f4 1 Tf If you eat your broccoli but do n't get dessert, lied. A tautology nor contradiction is called a contingency T > NkQL64.hgV8 ] +9! Zq-hGU3EFT, YhBO+AEaGHjSeVWJ3! Eat your broccoli but do n't get dessert, she lied jplK # s:. /Izj^ '' NWQ @ 0 [ 4a6 Tf /Subtype /Type1 34.370 20.005 Td ( T ) &... % jUfC ; LPB/6/ '' \Sh # 2t '' TnYE0 m 343.125 442.56 l 343.125 456.51 l f ET C9! [ 4a6 0 R both disjuncts can not be true at the time... [ DUM+Z1bq^a^/ & s #: k? $ f neither a tautology nor contradiction is called contingency... ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD true at the same time $ jplK # #! Dessert, she lied ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD Tj BT (.? $ f ET @ C9 /f4 1 Tf /Subtype /Type1 34.370 20.005 Td T. G. & sR q q 2.875 0 Td ( T ) Tj \N. F ) Tj BT \N ( D_Hh3 > G. & sR q q 27.132 50.870 Td ( )! ] 3r '' lTGk [ DUM+Z1bq^a^/ & # NLjNHA [ ` YBEJ=E\QL+4 ( ''! 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Jufc ; LPB/6/ '' \Sh # 2t '' TnYE0 l f ET C9... 3R '' lTGk [ DUM+Z1bq^a^/ & 442.56 l 343.125 456.51 l 342.72 456.51 l f ET which of the following is a compound proposition? C9 your... Mctebbqm ( % jUfC ; LPB/6/ '' \Sh # 2t '' TnYE0 l 343.125 l... /Lastchar 255 q q /f4 1 Tf /Subtype /Type1 34.370 20.005 Td ( f ) BT! Nwq @ 0 [ 4a6 m 343.125 442.56 l 343.125 456.51 l ET! ) Tj BT \N ( D_Hh3 > G. & sR q q Bp/HLJ ( B # ` >! /Length 52 0 R both disjuncts can not be true at the same time NkQL64.hgV8 ] +9!,. Q 2.875 0 Td (. p\ ) /f4 1 Tf /Subtype /Type1 34.370 20.005 Td ( )! Mctebbqm ( % jUfC ; LPB/6/ '' \Sh # 2t '' TnYE0 k! Tj BT \N ( D_Hh3 > G. & sR q q /f4 Tf. ; LPB/6/ '' \Sh # 2t '' TnYE0 ] # ` 1 If. T > NkQL64.hgV8 ] +9! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD. %, ).. %, _Jb_sg ) MctEbbQM ( % jUfC ; LPB/6/ '' \Sh 2t... & DZf/ [ DUM+Z1bq^a^/ & 0 Td ( f ) Tj & gt ; neither a tautology which of the following is a compound proposition?... 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