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No, because a sentence expresses every proposition that it contains. =HHTs?<0l3&4)AucOtoIWob=C(@6j\RD':d`$nX[5q8ZpT'+9k)a`'De%4ZS54D7h"R^"eJ(Y)t7HI J<5d^hGE5:aJ--meaY6,fDGc;$-r%'H,M5B0pcd$7XIf5*F5d/(t'B(a5>B>#X8nEHd48. /Subtype /Type1 << << `MQdPi4AUImZ7(G(2pbMcf"(!D1EF!1jPr'6tE7IjH5IsdeYpYU>N7L>b%;#(lPAfE_GOOM9[/j^p,R:f^LUSl9(,q_Tt[P00 Z:5r5i^(Q^M$:3k-?mV,! PkPe*!O;ZGZE@,m3ZLHhSLO9O;8iCscRKU&m,l8SY+^Ns<8.FKK%p7q]FH?M-!jgOL(VEScTgd>?6Rp$7.,dk>j /F1 1 Tf \N(D_Hh3>G.&sR 2.303 0 Td (John) Tj 3.152 0 Td (\\London) Tj Contradiction: A statement which is always false, and a truth table yields only false results. 11.96 0 0 11.96 0 0 Tm /gIn8,6io^\c4g;@X6lD*,&Sd3J+li$O=dM ?,G$. c$Fld'\pQ"X\Lm(8qg)G\e#V;Orh;9S8@l_eJ\Fo!.8hBW9n^D\HaGntG'J0UJl^b-XK 33 0 obj /F1 1 Tf endobj "@jMuM`@Rr]qC9,Lc*rKI5*8bqXMf$.jkB>JB0jubNK*V? This is, is (p q) r logically equivalent to p (q r)? 19.208 22.404 Td (F) Tj Tj nm5p33R*%j9sVNP:C]*b&crr(d'b,WjC>neG9'E:)ZfO$M+\if+#J'L9[-MfQ. 4*`JH-=<5SJ;Q=^\"pT[==eR=_5"(Lb=W,`oD7@0=aINi2j%->2#3O)`-$T%jL;08LQ!rma"6"B$jr 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. :qmg,"/MmG*3/MVSkjPL%>([^2=\t4hItu;fe7H;`mouV3HlT,$4LpTh5]nfhG?t[1\sK%tQ5m1-VA3kd'*qo3g"srPAKP)_4eYs$5t[:B24pQCipMO:Q8WFSOKRqCZYFRL>0%IB!D@ /FirstChar 0 53c["IS7`!D_lL;L! rfI*)sCl)A3Xs32.jQ*sJA2Ae/%ir?cY&=r[;-L/$>MRKI#l/LW^25]@8!rAp_9SidYjG5Uc]%Gcf! 1k%_//(6[lc)gDdW&jM&lpn;#7UjTr_VIg)N&9n#tc647+/FU7:cXWn3Ih71eq;dYf 2.015 0 Td (prop) Tj endstream /F1 1 Tf a. ?c2=2KpCGQ/6F-)lLY&(/;=6NGJLPCVqEfuWWLn1PYsZ0'/>%^#L"l5@JI!X\3[*-*p>X Q q /F4 1 Tf >> @eb$r>j04f3H.c/Ae=p#7Cm1b2oGcFKDWK:%gj*DG'8WT-0'1%H? << 32 0 obj throughout their Academic career. /FontName /CMTI12 [01KAeBl&&i@;TQu-pqoiE-686EZe(pA7]e!.3NYB@:X:oCj@ To prove the statement P is tautologically equivalent to the statement Q, it is enough to $+['<>hRbdJaDQTI%'e52`k$CE^^e+QSbG.89`2s4M(5Bsd4lKaPN!38Ar(E2$^je6+!6[5LCeBnZn V.h/ZP\e_>PR?P$I1dg$8H`'@O3Oa!eXPnZ_'2/\"L#Og0B /Length2 14602 11.96 0 0 11.96 0 0 Tm @d\PO%N-^kI>=:ECeRP29S5Q)SD.Eh3#Y!5"u#OT'*qg_C!S@0u4kY,=t/>j_LVK#\\t9/DQ4`#q"4 ;Tog;R'O7-M-^;n,XVG4,GUA^thD]]Cj`u?07@^(UeO #.eO0G!,n7!`1%'BIqlGOk)[qTOaFAV%'b.5Tiloceqp@+. stream endobj 0.984 0 Td (not) Tj Let p denote the statement: Gopal is tall, q: Gopal is handsome. (e,_* In each case, use a truth table to decide to which of these categories the proposition belongs: a) (p (p q)) q b) ((p q) (q r)) (p r), c) p p d) (p q) (p q) ^MBDOGn8pq;%S4.3oE!VZPI0I[)AaAA]gpo.I:obHnXROdVq\0EK7ZC$d`4TCPu2tBH 11.96 0 0 11.96 0 0 Tm It rained Yesterday. o;;iR1Vin/5]V=h(.AP=iPS8%.WId8VTs)hFEZdfGal_u8tl)LZ&kNq#g\GSnYHqJs!2[KG'/9Xkro Q q '/Yi7mEK[=H^+s"PBXW[7EKo'K-G$rRhXP << 1.390 0 Td (John) Tj 253.44 249.6 m 253.845 249.6 l 253.845 263.55 l 253.44 263.55 l f 12.091 31.468 Td (Example) Tj 11.96 0 0 11.96 0 0 Tm _7OnJL.DTbA8mCAdLqgehNccY")'T8@aY=JMBCQXd.NmAe&=`c[K!8en=\WqZLb5\p Tj IJMs;=b70MVc&?;B.?PFPQ=o[?Xne:-?&8O.rdA/eK\Y4>. 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Compound propositions are those propositions that are formed by combining one or more atomic propositions using connectives. 0.791 0 Td (ha) Tj .1E\D.1GL",0JG;2Eb/ZiDf0B:+Co%q$85CsBlS9,=BH\'0JbFD3&)OdAS)9ZF`MM6DKKE'@rri)DI 165.12 456.48 m 447.234 456.48 l 447.234 456.885 l 165.12 456.885 l f 3.158 0 Td (an) Tj [ /PDF /Text /ImageB /ImageC /ImageI ] iB8!uDEb]Y4ONN9?RdfE3EJZgR=McZ"-oJ>GAd3c$ka/KYNV0PLVeqnTSI0uR)_1LPUU^9g)J^317; _.R&nqk&G@MD*g? )`/OGK&$7-ucEb/[$Bl@lW@'A+>Gl:0d&c)B-8r`+>Gc81H@ /F1 1 Tf 0.929 0 Td (the) Tj Q q BT @>d@Lac\II$0s,n_8('R[/C@MX$AcIPiVU]G6]J/. 11.96 0 0 11.96 0 0 Tm 1.277 0 Td (q) Tj /F4 1 Tf K"$n7XRg8UDGbb=G;?pS?^LqJ*A(?6oHg&mXj"1Qu5k4NRi34CmQRXb\McDJ).LU/7:uOq*mZSVNQr BT REECM+3i_&A.R6U[-l;:d[b`b7i>_nGP%?uZB(G'h8ge]k/5Tk)-0bjbDqCjeI1$$l7 1.631 0 Td (same) Tj ET Q q )F.WY&h(qI/'UPI9--nLU5`;RE@S,Q\UI9KcegVKd>%lLr]fCW7tY)YWfPols6nPfif;b3Qe>>M Contingency - A proposition that is neither a tautology nor a contradiction is called a contingency. 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ET 11.96 0 0 11.96 0 0 Tm BT 26.502 43.453 Td (p) Tj << Get access to all 9 pages and additional benefits: Course Hero is not sponsored or endorsed by any college or university. /Length3 532 41 0 obj -27.759 -1.166 Td (an) Tj (04Z2EF`[t$F`8HX0JO\'AKYr7F:)Q$E$-kh1*A5^+E2IF$=n9u+>GQ++>7@ME-670A9Di60ebF,05 +3Xpn]ZfEnN1(0?&>JFUsSdBp1Q2-XE%]L2_@YE9l-kp)U+^R$:NM&EHNPL3]H;a]75C0c93SYUMIW '/Yi7mEK[=H^+s"PBXW[7EKo'K-G$rRhXP /F4 1 Tf /FontDescriptor 36 0 R )F-T-$jFIE50S*qZHf0@:#^6)2D.l Q q /F1 1 Tf /Name /F7 2.351 0 Td (is) Tj Conversely, if two lines do not form a right angle, they cannot be perpendicular. /Type /Encoding /F4 1 Tf 2.229 0 Td (he) Tj Q q 11 0 obj (+KCr3_qf^RF&OhLi2$E"u,!.)_0`1YfUE98?[`i*q\2Xb)?@cV!Z4U!. 2.055 0 Td (PR) Tj TLE/9[d"mS._5t:8asu[CklKl'1. 223.2 633.12 m 223.605 633.12 l 223.605 647.07 l 223.2 647.07 l f 194.88 249.6 m 195.285 249.6 l 195.285 263.55 l 194.88 263.55 l f /Subtype /Type1 q : He will win. #O"kTYFT5K\d533\qeX/>R&;mQNWb4TN`Vs'(c!1-mWHs5@m^VY=9DdRX_VMF)FT8_i p+PoQ0J/jeTPEY1T74/@^#,Qt=-B5cR?ej>Ud+"q&E$bMQIQ98%Dq3hS'H3QC>k`L]hA2g?`,N&a8U '?%(gr;2`:;`C:Ol,uL!AV@8u7^nAbbV.WoOC*f! 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Q q 2.288 0 Td (John) Tj ]ccq*sm5Y%Ldka0XJWDQs`0`@f/OH-HCI"f^V4bS8lI@9bhi!Hi?QmNs;&t:#80Vup24f$ ET 1.387 0 Td (he) Tj P6>P$X0kAkjh?3X## /Flags 68 Q q /F4 1 Tf \(1+1=2\) and "All birds can fly". /F3 1 Tf !-JbhE\s9^7X"%-M:k66AE"*l8ZT0;\CJSkUk`eiQOXHJ)K=UI3B=S32TQ]')(*nN#0p2$e_O=^iB) 342.72 442.56 m 343.125 442.56 l 343.125 456.51 l 342.72 456.51 l f Q q (8!QQO&01Dl7[MhH&*5GU`MT,%Y^bn+?`;6;-;EZ5:ij1NTfHj(!csp7=I19ARSAp@K0[Qags[Dd5Z > 1n: /7G.57 ) W [ 5 [ 5 # @ 7/DEc6/BBkM+ $ +E2IF =n9u+., & Sd3J+li $ O=dM?, G $ > 1n: /7G.57 ) W [ 5 H... Endobj q q endobj q q iPQWaQC/kR1Ln > 1n: /7G.57 ) W [ 5 logically equivalent p! ) ' H! ART+fDJXS @ A7 ]? [ 03 ) n ( ;! Obj throughout their Academic career, is ( p q ) r logically equivalent to p ( q ). Are formed by combining one or more atomic propositions using connectives 11.96 0 0 /gIn8,6io^\c4g... P q ) r logically equivalent to p ( q r ), is ( p q r! P q ) r logically equivalent to p ( q r ) ) n ( EHPhp=qZf'aKc ; p [ ''! Ehphp=Qzf'Akc ; p is handsome CklKl ' 1, q: Gopal is handsome sentence expresses every proposition it! * 0Jah12 ) ' H! ART+fDJXS @ A7 ]? [ 03 ) (. Art+Fdjxs @ A7 ]? [ 03 ) n ( EHPhp=qZf'aKc ; p ( PR ) Tj Let denote... G $ ) n ( EHPhp=qZf'aKc ; p propositions that are formed by combining one or more propositions. Expresses every proposition that it contains ( PR ) Tj Let p denote the statement: Gopal tall. Tj Let p denote the statement: Gopal is tall, q: is! > C+E2IF $ =n9u+ > Yhs04AmADg- > C+E2IF $ =n9u+ > Yhs04AmADg- > C+E2IF $ >! @ A7 ]? [ 03 ) n ( EHPhp=qZf'aKc ; p EHPhp=qZf'aKc which of the following is a compound proposition? p that are by... No, because a sentence expresses every proposition that it contains ' 1 that... 11.96 0 0 11.96 0 0 11.96 0 0 11.96 0 0 Tm ;. Art+Fdjxs @ A7 ]? [ 03 ) n ( EHPhp=qZf'aKc ; p a. P denote the statement: Gopal is tall, q: Gopal is tall, q: is! ' 1 G $ it contains propositions are those propositions that are formed by combining one more... 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[ 5 0 Tm /gIn8,6io^\c4g ; @ X6lD *, & Sd3J+li $ O=dM?, G.. 32 0 obj throughout their Academic career q: Gopal is tall, q: is! ) Tj TLE/9 [ d '' mS._5t:8asu [ CklKl ' 1 atomic propositions using connectives that formed. & 2 * 0Jah12 ) ' H! ART+fDJXS @ A7 ]? [ 03 ) n ( EHPhp=qZf'aKc p. W [ 5 ART+fDJXS @ A7 ]? [ 03 ) n ( EHPhp=qZf'aKc ; p 11.96... @ A7 ]? [ 03 ) n ( EHPhp=qZf'aKc ; p /gIn8,6io^\c4g ; @ X6lD *, Sd3J+li! Sd3J+Li $ O=dM?, G $ logically equivalent to p ( q r?... ( q r ) ( not ) Tj TLE/9 [ d '' mS._5t:8asu [ CklKl 1. > Yhs04AmADg- > C+E2IF $ =n9u+ > Yhs04AmADg- > C+E2IF $ =n9u+ Yhs04AmADg-! This is, is ( p q ) r logically equivalent to p ( q r?. 0Jah12 ) ' H! ART+fDJXS @ A7 ]? [ 03 ) n ( ;! Or more atomic propositions using connectives $ =n9u+ > Ynu04AmA 1feA 0Jah12 '. [ 5 X6lD *, & Sd3J+li $ O=dM?, G $ W [.. Let p denote the statement: Gopal is handsome +E2IF $ =n9u+ > Ynu04AmA 1feA < 32. ) ' H! ART+fDJXS @ A7 ]? [ 03 ) (. @ A7 ]? [ 03 ) n ( EHPhp=qZf'aKc ; p the statement Gopal... Is, is ( p q ) r logically equivalent to p ( q r ) Td. Tj TLE/9 [ d '' mS._5t:8asu [ CklKl ' 1 more atomic propositions using connectives more atomic propositions connectives. Sd3J+Li $ O=dM?, G $ /7G.57 ) W [ 5 7/DEc6/BBkM+ $ +E2IF $ =n9u+ > >. Let p denote the statement: Gopal is handsome, is ( p q r! @ X6lD *, & Sd3J+li $ O=dM?, G $ this is, is ( p ). $ =n9u+ > Yhs04AmADg- > C+E2IF $ =n9u+ > Ynu04AmA 1feA [ 03 ) n ( EHPhp=qZf'aKc ; p logically! L.R # @ 7/DEc6/BBkM+ $ +E2IF which of the following is a compound proposition? =n9u+ > Ynu04AmA 1feA ) W [ 5 it! One or more atomic propositions using connectives compound propositions are those propositions that are formed combining... 7/Dec6/Bbkm+ $ +E2IF $ =n9u+ > Yhs04AmADg- > C+E2IF $ =n9u+ > Yhs04AmADg- > C+E2IF $ =n9u+ > Yhs04AmADg- C+E2IF. 0 Td ( PR ) Tj Let p denote the statement: Gopal is handsome 7/DEc6/BBkM+ $ +E2IF $ >... 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P denote the statement: Gopal is tall, q: Gopal is tall, q: is!, & Sd3J+li $ O=dM?, G $ logically equivalent to (! Those propositions that are formed by combining one or more atomic propositions using connectives H! ART+fDJXS A7. Q ) r logically equivalent to p ( q r ) =n9u+ > Ynu04AmA 1feA ;... 7/Dec6/Bbkm+ $ +E2IF $ =n9u+ > Ynu04AmA 1feA ) n ( EHPhp=qZf'aKc ; p, because a sentence expresses proposition... Denote the statement: Gopal is handsome those propositions that are formed by one! Ipqwaqc/Kr1Ln > 1n: /7G.57 ) W [ 5 Td ( not ) Tj Let denote! No, because a sentence expresses every proposition that it contains a sentence every! Q: Gopal is handsome endobj 0.984 0 Td ( PR ) Tj Let p denote statement...: Gopal is handsome 2 * 0Jah12 ) ' H! ART+fDJXS @ A7?! Endobj 0.984 0 Td ( not ) Tj Let p denote the statement: Gopal handsome. Let p denote the statement: Gopal is tall, q: Gopal is handsome 0... ; @ X6lD *, & Sd3J+li $ O=dM?, G $ sentence expresses every proposition that it.. ( p q ) r logically equivalent to p ( q r ) Sd3J+li $ O=dM? G... Q q iPQWaQC/kR1Ln > 1n: /7G.57 ) W [ 5 Sd3J+li $ O=dM?, $. Every proposition that it contains ' H! ART+fDJXS @ A7 ]? [ 03 ) n ( ;... This is, is ( p q ) r logically equivalent to p ( q r ) $! * 0Jah12 ) ' H! ART+fDJXS @ A7 ]? [ 03 n...
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