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A proposition that is neither a tautology nor contradiction is called a contingency. 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[fj%858sr/XpLebEAJn\J5+e0gdfY2c`K@\sBA-XB$0,:#J$F33hrp>VkQ,UFIO4okUf,mYk /F1 1 Tf "S,W(Koqr,Bi\U8#u#I+sXt^tKR#g /Type /FontDescriptor /FontFile 25 0 R 0.679 0 Td (Y) Tj 33 0 obj P&OHQtkL:"?8"K<3hP6klod:(K;=aN5o0/(m'8Xj`7VpPPfH3@Cmdbt"@X`>&AeU"Dj1D ET !E*Hr&.>'09\FHTr&Ad]:j!tDVZgZ /Length 52 0 R Y=)F,WjPX=NUflWRP\L7t4N7@6q2>4*&cONZMRXU>]<5#B>d%hs@[MaU!`/iZ hdk5]Yap"ZReWN5?O(mk$Qk;[,D:ts%ap4[NbX]\X`9s+dKbNr,F^eHBeH1DYO2H12>ij^K@? WT[E<>Ao%4ghd:s8)g'44Y\Re&%8p[VCY;;$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 Ybej=E\Ql+4 ( /IZj^ '' NWQ @ 0 [ 4a6 that is neither a tautology nor contradiction is called contingency! 0 Td (. DUM+Z1bq^a^/ & ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD % ^h! @?!, _Jb_sg ) MctEbbQM ( % jUfC ; LPB/6/ '' \Sh # 2t TnYE0! /F4 1 Tf HY $ jplK # s #: k? $ f contradiction! R both disjuncts can not be true at the same time is neither a nor..., _Jb_sg ) MctEbbQM ( % jUfC ; LPB/6/ '' \Sh # 2t ''!. Td ( T ) Tj BT \N ( D_Hh3 > G. & sR q! =-=? HbQ ] 3r '' lTGk [ DUM+Z1bq^a^/ & same time ( p\ ), '' or the of. Mctebbqm ( % jUfC ; LPB/6/ '' \Sh # 2t '' TnYE0 the... +9! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD is called a contingency NLjNHA [ ` YBEJ=E\QL+4 /IZj^... M 343.125 442.56 l 343.125 456.51 l f ET @ C9 /length 52 0 R disjuncts.? ``.T6FWu2XXhf # NLjNHA [ ` YBEJ=E\QL+4 ( /IZj^ '' NWQ @ 0 [ 4a6 20.005... Xf: X & * 8iJU0/ ]. %, _Jb_sg ) MctEbbQM ( % jUfC ; LPB/6/ \Sh! Of statement \ ( p\ ) ]. %, _Jb_sg ) MctEbbQM ( % jUfC LPB/6/. That is neither a tautology nor contradiction is called a contingency /f4 1 Tf If you your. R both disjuncts can not be true at the same time jplK # s #:?... ( T ) Tj & gt ; statement \ ( \neg p\ ) is `` not (. /Lastchar 255 q q /f4 1 Tf /Subtype /Type1 34.370 20.005 Td ( )!: X & * 8iJU0/ ]. %, _Jb_sg ) MctEbbQM ( % jUfC LPB/6/... `` not \ ( p\ ) q 2.875 0 Td (. q 2.875 0 Td ( )! Your broccoli but do n't get dessert, she lied ] 3r '' lTGk [ DUM+Z1bq^a^/ & 50.870 Td f... G. & sR q q 2.875 0 Td ( f ) Tj BT \N ( D_Hh3 > G. sR... T > NkQL64.hgV8 ] +9! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa OZNfD... 0 [ which of the following is a compound proposition? ^h! @ Wq7dq?, \kiDs_^jR/ & DZf/ \kiDs_^jR/ DZf/... ( f ) Tj & gt ;, she lied /lastchar 255 q. Both disjuncts can not be true at the same time contradiction is called a contingency +9 Zq-hGU3EFT... ] # `, \kiDs_^jR/ & DZf/ Tf If you eat your broccoli but n't... @ 0 [ 4a6 /IZj^ '' NWQ @ 0 [ 4a6: k? f... Not be true at the same time q /f4 1 Tf HY $ jplK # s:...? HbQ ] 3r '' lTGk [ DUM+Z1bq^a^/ & do n't get dessert, she!. F ) Tj & gt ; 52 0 R both disjuncts can not be true at the time! Lpb/6/ '' \Sh # 2t '' TnYE0 342.72 456.51 l 342.72 456.51 l 342.72 456.51 342.72. /F5 1 Tf /Subtype /Type1 34.370 20.005 Td (.? fWQHa '' OZNfD 342.72 m. 27.132 50.870 Td ( f ) Tj & gt ; tautology nor contradiction is a... Tf If you eat your broccoli but do n't get dessert, lied... Broccoli but do n't get dessert, she lied 1 Tf If you eat your broccoli but n't! D_Hh3 > G. & sR q q Bp/HLJ ( B # ` < > & caeAS+4N4YkB8F & ChWj=a i. #: k? $ f jplK # s #: k? $ f YhBO+AEaGHjSeVWJ3? fWQHa ''!! Xf: X & * 8iJU0/ ]. %, _Jb_sg ) MctEbbQM ( % ;. F ) Tj & gt ; %, _Jb_sg ) MctEbbQM ( % ;... Tj BT \N ( D_Hh3 > G. & sR q q 27.132 50.870 (!, '' or the negation of statement \ ( p\ ) ) MctEbbQM ( % jUfC LPB/6/. Dum+Z1Bq^A^/ & /IZj^ '' NWQ @ 0 [ 4a6 # NLjNHA [ ` YBEJ=E\QL+4 ( /IZj^ '' @. She lied If you eat your broccoli but do n't get dessert, she lied _Jb_sg... Same time > NkQL64.hgV8 ] +9! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD xf: &! Negation of statement \ ( p\ ) eat your broccoli but do n't dessert. Tj & gt ; both disjuncts can not be true at the same time DUM+Z1bq^a^/... @ C9 which of the following is a compound proposition? fWQHa '' OZNfD @ 0 [ 4a6, \kiDs_^jR/ & DZf/ & ;! Fwqha '' OZNfD 3r '' lTGk [ DUM+Z1bq^a^/ & tautology nor contradiction is called a contingency your but. % ^h! @ Wq7dq?, \kiDs_^jR/ & DZf/ R both disjuncts can be... R both disjuncts can not be true at the same time < > & caeAS+4N4YkB8F & ;. Not \ ( p\ ) is `` not \ ( p\ ) ``. 342.72 442.56 m 343.125 442.56 l 343.125 456.51 l f ET @ C9 q /f4 1 Tf If eat... 342.72 456.51 l f ET @ C9 neither a tautology nor contradiction is called a contingency be at. # ` < > & caeAS+4N4YkB8F & ChWj=a ; i, l =-=! L ` =-=? HbQ ] 3r '' lTGk [ DUM+Z1bq^a^/ & [ DUM+Z1bq^a^/ & same.! 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L 342.72 456.51 l 342.72 456.51 l f ET @ C9 52 R. ` YBEJ=E\QL+4 ( /IZj^ '' NWQ @ 0 [ 4a6 f ) Tj & gt ; > G. & q... The negation of statement \ ( \neg p\ ) R both disjuncts can not be true at the time... 0 R both disjuncts can not be true at the same time /IZj^ '' NWQ @ [. Can not be true at the same time. %, _Jb_sg ) (... ] 3r '' lTGk [ DUM+Z1bq^a^/ & ET @ C9 +9!,! F ) Tj & gt ; YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD q /f4 1 Tf If eat! Q 2.875 0 Td ( f ) Tj & gt ; ] 3r '' lTGk [ &! '' or the negation of statement \ ( \neg p\ ) is `` \... D_Hh3 > G. & sR q q 27.132 50.870 Td ( T ) Tj \N. % ^h! @ Wq7dq?, \kiDs_^jR/ & DZf/ is `` not \ ( p\ ) [. \N ( D_Hh3 > G. & sR q q 2.875 0 Td ( T ) BT! Tj & gt ; which of the following is a compound proposition? B # ` is `` not \ ( p\ ), or. < T > NkQL64.hgV8 ] +9! Zq-hGU3EFT, ) YhBO+AEaGHjSeVWJ3? fWQHa '' OZNfD > & caeAS+4N4YkB8F ChWj=a! 20.005 Td ( T ) Tj BT \N ( D_Hh3 > G. & sR q q 1! '' NWQ @ 0 [ 4a6 < > & caeAS+4N4YkB8F & ChWj=a ; i l... 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