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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$rRhXP << 1.390 0 Td (John) Tj 253.44 249.6 m 253.845 249.6 l 253.845 263.55 l 253.44 263.55 l f 12.091 31.468 Td (Example) Tj 11.96 0 0 11.96 0 0 Tm _7OnJL.DTbA8mCAdLqgehNccY")'T8@aY=JMBCQXd.NmAe&=`c[K!8en=\WqZLb5\p Tj IJMs;=b70MVc&?;B.?PFPQ=o[?Xne:-?&8O.rdA/eK\Y4>. 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ET 11.96 0 0 11.96 0 0 Tm BT 26.502 43.453 Td (p) Tj << Get access to all 9 pages and additional benefits: Course Hero is not sponsored or endorsed by any college or university. /Length3 532 41 0 obj -27.759 -1.166 Td (an) Tj (04Z2EF`[t$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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[ 03 ) n EHPhp=qZf'aKc. # @ 7/DEc6/BBkM+ $ +E2IF $ =n9u+ > Ynu04AmA 1feA using connectives are...: Gopal is tall, q: Gopal is handsome ( p q ) r logically equivalent to p q... ) r logically equivalent to p ( q r ) equivalent to p ( q r ) Academic.!";s:7:"keyword";s:49:"which of the following is a compound proposition?";s:5:"links";s:781:"Lawrence Ray Extra,
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