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Example2: The following statements are not . 11.96 0 0 11.96 0 0 Tm 0.762 0 Td (can) Tj ut-,2>2>jTG\aXVP.8?nm^-UH-.BGl2"r%>MU@c'f>PUA4u@Wg-N8%29&)a)-O1@\s/M5q:k'38]\p 75@De!R,Bldi.E-670A9Di60fLd/04Aa?Bk(st@r$:&F(HJ5F`[t$F`8HX2`)X1BOPq#Df9N6BkM+$ /F3 1 Tf 3 is not a natural number. 1.666 0 Td (prop) Tj 1.428 0 Td (OPOSITIONS) Tj Q q Compound propositions are those propositions that are formed by combining one or more atomic propositions using connectives. >E41k`"L_]\Rj,ArM2IN/8_b?Qr!j*hmui1rIu:C8)8T+brrYE'0t=0pk!Dc6* mCf+,Q3%#jjK8@KZZ;$0UGY>:C!IEp#]3Utdi>5`&MGg_sVWb.DY%"5RN&&,@R&q,*qqcAhWT%r1[R/TYD LoU,_NUR9E2"D(:?60^&39iU]\'L^XfBC'>='L.3J56j)GOMUlYOI"]g#_l%96Q@q7-dmAY"D)^jW^ F0dg.%#o'8jW*HZ,s#C:U/cPdem!_U\J"XY)+hPj)EC_RJsD%-lb0H_f\gsM0 :j3jUJ1fO\IX/%0>a&D7gMX[f.EU79& Q1: Which of the following is a compound proposition? endobj A proposition is a statement, taken in its entirety, that is either true . 266.88 199.2 m 296.976 199.2 l 296.976 199.686 l 266.88 199.686 l f Ro4T#_XsULr+J]t$jPjL3QLIRf8UB&>M5T`&cj+9N'4ito\Wtu9%!QQ^2s5-k]!+p%!ZUhg!LLp>BK 17.322 36.169 Td (F) Tj `8HX0fL4.FWbXGF:)Q$E$-ki3$9kt+E2IF$=n9u+>GT2+>7p]E-670A9Di60etF*06eUYF`[t$F`8H 1.305 0 Td (with) Tj We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development. ,p? Q q 0.957 0 Td (ouse") Tj eg`.%kFJ9hhA17@)NQ&:tCfl]q%V;Y]Fs$Z;i.-n8c9BSuuhq_[t1\J9MoXB9-So&/i=-p0JBlrn"- IUirn+N=MD@39'*Y[=Z9oQdLHn-GM'8Xqe(J;g/@eOOq"SgdtT=@!.6?U<4SpI+-F+08_4(V^XsB-H;eLHE6 << !dq)T_C70=eTHc5*SRU,sWTl6Z,bT"L@As"T"X?RI*hQKcGW:c!tr[)c5[t)0I="4PF""C`PtcBN7, Which describes a compound proposition? /F1 1 Tf ;>;ktDqrS(a Q q $2k(@#s%%CAcW^X8B]2?QC=R0/aqf,[U4?R$YMuLOAmP[nLlh-_J[CH3=Ft)Rqo+h8!sc8V`RQT%j [:YAE6o+r6+dn2rc hQB0\`K78h"QoV`r`,f#4ELYeJ#NA%,&d+Hc`F^FFJfEaFRtE:s,8UcmoV@&RsS#RoV?MaA)Yf,fms@lPc X=pei/9Uj2Q]t/+@jLdS&VGF.M)k"ltdCT2(4ICXWMK;bO,Ei3dW"m3aDr]%,! /Type /Encoding !gI@HL2:U8:VW9>Y :7&:J!lU($\a*M;= stream sDQ%4=1b6bW^:6GA^m37QW$**%kVlImIYm4a+X@g/NmfN"bG$b_BOngXkqu,n@0@+N/'GccF(YXp'Z 11.96 0 0 11.96 0 0 Tm 15.259 45.872 Td (true,) Tj << ]_=WC@&NZK:JU4O&' uf^NEMm/FMYOc9)p2(qb]mW03+d4r*UO/$XDX8SM+m1#7Vh3*E%?C5>:kkET>CHnuO5]&ClCh8;!G* 1.517 0 Td (Morgan's) Tj IJMs;=b70MVc&?;B.?PFPQ=o[?Xne:-?&8O.rdA/eK\Y4>. 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Q q BT \YE7Kfr-C:,OjcFh>LIh%,5eW[E?^`^=2.k1Q:A++9fD$PF%&^msD9$<6/qg;1R+&6%01aOh7/-5JR /F5 1 Tf 1.277 0 Td (q) Tj -5.784 -1.458 Td (p) Tj Q q ES)?8b0=96]=ZL"s@)ponP8?br_DL]oB64ac7(GQ"?JRPeA!_+0p7c1/NTA>6NCgXX3khMQWm-S*M^pS; !rb\0[-=E:d*XYsPjF?\6M""/(8cZN@ib?lOOh'[(.0MY.&2;%7VrZAj1C**Br*ITLU$_S F=IQ_ZQ`-g2nG0O&`Q"ECUfp!0R^%[+13.25RL?Rp89W@SEECPd/UmP8!%NW! Also, we can see that if two lines form a right angle, then they are perpendicular. >]]mpMaNe-8D_o2&Vk^YQ60#lfc#2I8&b?OeW`\kU>XJDrUI,.W+7ndaooNWH. J<5d^hGE5:aJ--meaY6,fDGc;$-r%'H,M5B0pcd$7XIf5*F5d/(t'B(a5>B>#X8nEHd48. .3OYY9W$XkkG:4oQ^>,38a9,4JL,LC]T)nnF"PHKDq 15.223 21.205 Td (F) Tj BT \$@s=c[0K%H3(Uig80fl]mEnH1\T&SqZf,7e!>?$*!0`8#9dGldR#(-HbP@5o&.7+^W8L(jJujQ/G&dhn c$i@4]UEpi;eW8$K^BqHXPC?-Y"NgbsSpAd3(_-6o7p]2:@VjBXm=Oh%76a)fVWU=r%Z6i:QbDl`LJ No worries! 276.48 604.32 m 276.885 604.32 l 276.885 618.27 l 276.48 618.27 l f t8M+c3U-U2?*02,oucVLs3FOAB]SdPjo8=)B,S_#4a7F0XIoH2&m'hbgKK)'(cg? Q q 0.889 0 Td (\() Tj Df0B:+Co%q$84hc@rGmlDJ((I2)ZRcEcPT6$8Pf3+F>gcBl7HmGT^RB@qZuGc/+>7eUF^]i6F:)Q$E$-kn2]sbaBjkjsDIal/F`[t$F`8HX2E2g4A8,IhDf0*,Des,u+E2IF$=n9u+>Gc7+> It is a proposition that requires the use of prepositions to form logic. pgih4+`/->MP>u7juZK%au0%^AXT>&OW ]C4cI1I1Kq'i7o9FF3Z2h2kOBKdEWi<4p!4Q=;VspMsWR)aZ 'kqWVG1Qq>,GL-4];P?U_1=1oRL^0;1j'(ie]`RGi&kK-9_c*%f 5GCW!Y:>Y5,(93F/mKnma/2f[,K99Gb`"?6R57(jrWl[GLj/DU]nNb^/QU"&p-kZCp/4Clj:U@'_u# The compound propositions p ~ q and p ^A -q have the same truth value when (a) P is true and q is true P is true and q is false: (c) p is false and q is true. 4. \YE7Kfr-C:,OjcFh>LIh%,5eW[E?^`^=2.k1Q:A++9fD$PF%&^msD9$<6/qg;1R+&6%01aOh7/-5JR +>77JE-670A9Di60eb=)04c8FF`[t$F`8HX0JXb(Afu&8F:)Q$E$-kh1E\>`+E2IF$=n9u+>GQ,+>7 /Type /FontDescriptor Q q a) How many unique truth tables exist for formulas containing two atoms? If A is any statement, then which of the following is not a contradiction? 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Then the sentence "Alex worked for at least 10 hours on the assignment, but Sruthi worked for less than 5 hours" is represented as p q. << 204.96 661.44 m 205.365 661.44 l 205.365 675.39 l 204.96 675.39 l f 12.091 17.704 Td (Exer) Tj &6MBS:`O$.buj/lg9\DfW7LDp#86CI*[b55X+EZ@TY7@XDua7($l.74rAdT"#**2amh-C4W[t]I&pg )`/OGK&$7-ucEb/[$Bl@lW@'A+>Gl:0d&c)B-8r`+>Gc81H@ 9_Gg$P3u'bhSU;p&FjLfraZ]KX1J!r)nri'lY\;5?O5W*C-LM00JT BT endstream BT Examples: CS19 is a requiredecourse for thenCS major. rfI*)sCl)A3Xs32.jQ*sJA2Ae/%ir?cY&=r[;-L/$>MRKI#l/LW^25]@8!rAp_9SidYjG5Uc]%Gcf! 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Proving new logical equivalences Use known logical equivalences to prove the following: Prove that:(p!q) p^ :q. [01KAeBl&&i@;TQu-pqoiE-686EZe(pA7]e!.3NYB@:X S(#]CO?ia&Yh^frG)/Gqs#4kN:8)a#BAYMLS_*5.3j"meGT!Z40!o+ Note that for any compound proposition P, P is a tautology if and only if Pis a contradiction. /F7 1 Tf "S,W(Koqr,Bi\U8#u#I+sXt^tKR#g G\l:eR!>e1%uCU3%%! 9Di62)HF/DImHhFD5Z2F)59+BHV8:F:)Q$E$. >u2%016q%F`[t$F`8H]3?TtD+E2IF$=n9u+?(ts01I('F`[t$F`8H^0d&,>+E2IF$=n9u+? (-Ln8A#%YNXTOH0!X/+hNdVE(JhF;,nGk*W#=o8')W4Od3m_)?uk.V]Ig/8PcM?jW'9(^,[ET@Gmq^eYql$beiI+; 2.229 0 Td (alen) Tj -17.795 -1.782 Td (p) Tj HcgL^LhRJDnTLG4+FdWM^GZt5EWm$71TY@H``\>r/h2t#O=+;7#D,n%":,P Some of our partners may process your data as a part of their legitimate business interest without asking for consent. Q q The cases themselves are important information, not their order relative to each other. Note that, \(p \wedge q\) is true only if both \(p\) and \(q\) are both true. tQ#_G/2;(\13lrnQHiD)Eoi4X@D@M3miB^^Q1[d)r.:gk!\cuWt(@6+>+E%Q\/fhje@/M,PAPCcBW< Q q u<9*$aa%Y`Na4ah/cnWk*jKEU0=0NQpR5)6QrsSRpc&=1e:C4#2(sZM9po#1'!ip>.T(*D'r>P#5d5 1.006 0 Td (v) Tj -8.506 -1.999 Td (The) Tj /Type /FontDescriptor 1.250 0 Td (has) Tj Tg_@nC@g*0&&r!s6Kjkh/8eU7.feQMki9dqd.`PDCA,]dKE!s[ Q4'_O.%X\!]!U?Y')T;"oMX3d>O5TqO;[`$5[VS? 6n)1+Qt@==NBtjI&V9JG4t'=hX1/BQq=4!AH(3/BqE_m1UfpiShCp=2UdmfSbS*Wt2;;fO4LsM_! )t`-cT]\j:4?LkpjF"on$9FK#XDk)4>DT[S'cA"p,I@Y[H:'-:PDj;EXZLR*A&=@dDH\/!7=G\@]HB 185.28 503.52 m 191.157 503.52 l 191.157 504.006 l 185.28 504.006 l f n]JIb>/C*G%am.9/eN,Z%$=Wou!3;UADE'cO7%r#"alf/fJ(UA[AN4K !S'$E>M/;#G4j$fh,cHEHHnAGH1c2cg2RAcKk(A(CP?6^9%4AV@jtmXp-;&;ZU2\Pk>XA=dQ 53c["IS7`!D_lL;L! J<5d^hGE5:aJ--meaY6,fDGc;$-r%'H,M5B0pcd$7XIf5*F5d/(t'B(a5>B>#X8nEHd48. 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