/Length2 10935 L`Cd:J0m`V6la_#g+Ku)?M*\4*,Bim68Glc03?SdfbkjsB_LMtHU2/tG%R`;:"rCfg!2!s>ihiRTLg 2.311 0 Td (Illinois) Tj -6m=(Gq! GGZpF`Tm@!0@'coa7\p!M2=2'_k64rOMBB+Tm@m]Bp8&"p_9DJ(U8lg!#-HN>:t[oqqHcO^QgQMggcg^C; B"mp#R`F^D"sXrL0g^J49I(DH-EF`kc/ame"g9g*/9eAY%CpOr2gU-19.O$mn9u%8`=]le^&Joh)!) 1.798 0 Td (the) Tj /Type /Encoding 0.917 0 Td (q) Tj Q q 2.629 0 Td (e.) Tj /F1 1 Tf Tj 11.96 0 0 11.96 0 0 Tm Q q /Length1 2008 1.278 0 Td (q) Tj Nn@F:)Q$E$..r+>7GHFCfK6ARfgrDf-\:F`[t$F`8H`1a"GfDeEco@;K@iA0>i6F:)Q$E$..u+>7PL "Polygamy is bad." This is a "moral" statement that is neither true nor false until its context or standard is specified. `A7)SCdok*QYi.g0J8'5J)rh7b_kZ%]t3[/(=5^-=R !-JbhE\s9^7X"%-M:k66AE"*l8ZT0;\CJSkUk`eiQOXHJ)K=UI3B=S32TQ]')(*nN#0p2$e_O=^iB) Q q 1.277 0 Td (q) Tj e;lB^?IcS3Tb6+hu77o7hSpQ2bO*E$NMo?uuM?_P$*QS@sgOArG-6cf7%7:V! 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'fp5E5,`pBC'G)n&mWH\?mg(3?m-0:%KtE=FhI"XAK'mEib@qO=+9HI9;u"P7Cjl@6A2s IIWU_XO!qGAf\I&Fkj;Ka8qtd3H'Edcqj%,aKp;b/,R8kNk[r^Q`0 2.311 0 Td (Prop) Tj 4.383 0 Td (t) Tj Disjunction statements are compound statements made up of two or more statements and are true when one of the component propositions is true. 11.96 0 0 11.96 0 0 Tm /F5 1 Tf 219.84 442.56 m 220.245 442.56 l 220.245 456.51 l 219.84 456.51 l f )s 11.96 0 0 11.96 0 0 Tm $[qF`M"Y`WeHQ`:j@Q\Tr=3ThR9uMudA;^^._uA8s!0m[T0%5Hcu'FjI@k)V=$Z The reason why this is correct is because it's a compound proposition. 32 0 obj /F1 1 Tf /F4 1 Tf << c5F\`V[1'a'.tKKQH7:PjApfm)0(M[q2Tq6?^4qT3H2CbTtFlN]H*]V9GDjsg lC.$4Y()"tVDZdHf\B7erWr.GVh6OPC[*(XJY80>qL,aK'7mo^>_]a. /Encoding 31 0 R 11.96 0 0 11.96 0 0 Tm 31.128 54.110 Td (\)) Tj WN#SP*60]Fr'9@Bepe?`*RQ!D[upTaJAcGq$WU!9;+$5f`/TWShdrQAPP@(5N/N\C4>hW'1RAb5I>+5m=Ou"LPq> Q q ?5[kb64NgcX%ddp>Gr?$T'0PhuuDK`pSA/'"AjHN'^9a/aYQ6oh'\p(@^Y?RL5AmqopX+MdW:./?o_ 33 0 obj 0.749 0 Td (F) Tj ET r%:%PB(uC^!`1K(g2(iY7Q? BT 1.151 0 Td (al) Tj :AaCo-[I:3^!A. hBPf/=Y! 33.579 52.069 Td (F) Tj \N(D_Hh3>G.&sR endobj V/F+2T(5V3a`'?%c4(! ad$][G%agN7Od_AD(>'43kAi+_,Ml#61]mAY9g0=r6(,Wul0e0m8`tH?5EBO]G/Gq58u>kP ?/8o4)N*VV$[$S"1Tr6-Pd@, 4 0 obj g]q(Z"T,/%.MIC)J,,b&k/?=^"lom50f-dNXdY[_?1Cs;cML9)?=YGBfJ6=F:_HDT(tKf&IU"cjl6> endstream Which of the proposition is p ^ (~p v q) is, Let p denote the statement: I finish my homework before dinner, q: It rains and r: I will go for a walk, the representative of the following statement: if I finish my homework before dinner and it does not rain, then I will go for walk is. :AaCo-[I:3^!A. 25 0 obj BT GKpi0.ME^Q02TY#J?IXSr8bK&uq7%?L-QD$tsQs_ t]'a-Pn6,7\WN]=i_kKH8@p0@qLbMlL#? It is either true or false but not both. 385.44 661.44 m 385.845 661.44 l 385.845 675.39 l 385.44 675.39 l f ZVFC&? SV;>I2DQqSi^H\@jqUjD:SQ2!pft@,0j^2]ZmHDA5"LAR%_XXjj_JBZU.M["m@K(h(aj:t9KGqq\FN 11.96 0 0 11.96 0 0 Tm 1.401 0 Td (John) Tj Because of this truth functionality, it is possible to compute the truth value of a compound proposition from a set of initial truth values for the simple statement components that make up the 0.848 0 Td (ying) Tj o;;iR1Vin/5]V=h(.AP=iPS8%.WId8VTs)hFEZdfGal_u8tl)LZ&kNq#g\GSnYHqJs!2[KG'/9Xkro BT /Type /FontDescriptor )5%023R.F`[t$F` 194.88 235.2 m 195.285 235.2 l 195.285 249.15 l 194.88 249.15 l f R_hu/XY+^KY7LThVgnJCn)]J^]kBo:qfqU!K.NTPlq:&NDQ+A@9r/T_]1qneC:eBkQ4J+_0[(GSiD> 412.32 399.84 m 412.725 399.84 l 412.725 413.79 l 412.32 413.79 l f U^'20P^hC%4@l6R8kDO.0B7.p.S2h`BG%)C,OHlE/Wf/rUFH.^^/m. /FontFile 41 0 R /FirstChar 0 \O=Q^t0`_H4DB!q6#16q$*k.G6. So: \(\neg p \vee (p \wedge q) \equiv p \to q\), or "Not p or (p and q) is equivalent to if p then q. BT /StemV 20 Q q >> 38 0 obj $+['<>hRbdJaDQTI%'e52`k$CE^^e+QSbG.89`2s4M(5Bsd4lKaPN!38Ar(E2$^je6+!6[5LCeBnZn ^Jtu-.42c\aO,ES=lks6+*]oa1F8+8Kg9QNVS.EqpSTeJZjnI,_?n4OJB4NW( B"mp#R`F^D"sXrL0g^J49I(DH-EF`kc/ame"g9g*/9eAY%CpOr2gU-19.O$mn9u%8`=]le^&Joh)!) 1.740 0 Td (from) Tj endstream 15.297 24.803 Td (p) Tj ET @:t^Q"3Sa"=@nSE(H_6cKKl[Fe0lIfLi-t0a, /F3 1 Tf @;>"gX`6m*k>m2]FSTt^S82(q << M'704ng4+E2IF$=n9u+>Gi0+>78DFDPN0F(uh:F`[t$F`8HX3&)O/B6%F(AKYr7F:)Q$E$-kp1*A5Y Either x is not an even number or x is divisible by 3, but not both. 273.12 456.96 m 273.525 456.96 l 273.525 470.91 l 273.12 470.91 l f jpHKk'"R)mj[f.;pKQpL1"frJ)$-Ti6aUN\!A5J8K+DU.ns4GT[O5=si&n'T$Z#\.Aj(TQQE2E6Il] )`/OGl:2]tD'ATDKp@;[2^@< /CapHeight 705 A proposition that is neither a tautology nor contradiction is called a contingency. a)aF`MM6DKKK)Ch4`#AU%cr$@jsYJu^mufeD>uV[X)+0cb7qqCN@A=>;f0AsHAVHKd8G2p0-O(^A? ;jGAM1u%!G\X9,JXAVl5;'LO8l';#oDrAnMAsc,^DS9C_gJYGmC;8BYF;%n$j[>TMCZs6lVgHjh^ML /Dests 5 0 R .1E\D.1GL",0JG;2Eb/ZiDf0B:+Co%q$85CsBlS9,=BH\'0JbFD3&)OdAS)9ZF`MM6DKKE'@rri)DI %J=2c3nM>?#^!RW@eV&6qI"2SGRm;b)dJ*Z@TG^T[-[A8S4'K4UNE: Q q @VFYq#Wl=gH]8 Q q BT /F1 1 Tf BT The symbolic form of "He is hard working but not going to win", is. Q q /BaseFont /CMR9 1.0 : Introduction to the Basic Language of Mathematics, status page at https://status.libretexts.org. 0.856 0 Td (non-exclusive) Tj @(DEb/ZiDf0B:+Co%q$84hc@rGmlDJ((I2)ZRcEcPT6$8Pf3+F>gcBl7HmGT^RB@qZuGc/+>7SGDKU"CE-670A9Di60fCd005tKCBl@NlASuU$Eb/c(E-670A9D /Length3 532 KktF@&<4G^D#"1E\8)2)-4.0f(g42`3:;Eb/ZiDf0B:+Co%q$85CsBlS9,=BH\'0JG1>2E;mjAS)9Z BT )%u01[4 @ 11.96 0 0 11.96 0 0 Tm 15.521 47.459 Td (is) Tj 0.816 0 Td (sp) Tj 0.713 0 Td (^) Tj /F4 1 Tf Q q 53c["IS7`!D_lL;L! /gDWDqR'K(<7LNlRCYRkTAGQ^Br[n6dQ%i^/qY'#!63PM_ZBh?a1$K8]Dqns7HmYVSH)$07+hKRhI: ET 11.96 0 0 11.96 0 0 Tm 11.96 0 0 11.96 0 0 Tm [Hi-.<9IKA23c[\;- r%:%PB(uC^!`1K(g2(iY7Q? ,OB$=SJXDs4#qS!PZ?3jk""?$mUpd:?&PKFsW1n]glE3R4_PF1#1,,/X3ltECH2q^9E;)139fuI0-L qj4aqF]W8QtoFoHq`ej/u6>K)c*H=Q983`^Sfh@@r/+#XH'>9g?ar[ZUULWLWp [4"4&8W6qN)]CcT[aNbuO`%M ]=ptWiN\'5mW(dAE8gN5&T-dh?WZT5(>)ieU@c?_QSTbGHhD*M1THI)+oDT`\TOt/hQehFgl6r5]rj60O\^$>eZ=ImEL8(emJ&ua#`+f ]=ptWiN\'5mW(dAE8gN5&T-dh?WZT5(>)ieU@c?_QSTbGHhD*M1THI)+oDT`\TOt/hQehFgl6r5]rj60O\^$>eZ=ImEL8(emJ&ua#`+f 12.091 17.704 Td (Exer) Tj ET A F: c. A F: d. None of mentioned: View Answer Report . L:o2W@JDq_[=R!k9EO%H%LeC^DXO$<1",Tdd0=:ro]=cXp!P7ZqobS8fRd%pj-Y#D&`-MO0Jofa1U' Q q a5Z?".T6FWu2XXhf#NLjNHA[`YBEJ=E\QL+4(/IZj^"NWQ@0[4a6. /F1 1 Tf Q q QkTr,l;u>U!p3!ehN9[V86d&l]i+D%,'0CH[PXk`&G>(To:L3lUrP3[ba`;eYHnI!QTG3h1IJ'6nCH ;>;ktDqrS(a 4.980 0 Td (prop) Tj We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development. )`/OP0ea_*/hm\Z,su]a@4%DF@oTANCqg3B8l.DKKqBG@bf++Co&)BkM?,+EV:.+@0jUEbT#lDBMY^FD,6&@ (W"h:g&]3-rFOtZ>tqohV8h6fFW\QS'c$YC>8)AopQ*4_IlPt\TH)W_F6bm/=q+WFBuNfStob==fFK /F1 1 Tf 4.149 0 Td (sa) Tj /Widths [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1000 500 0 1000 0 0 0 0 1000 0 0 1000 0 0 0 0 1000 667 0 889 0 0 0 556 556 0 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 667 667 0 667 667 0 0 444 444 444 444 500 500 389 389 278 0 0 0 0 0 833 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 778 278 778 500 0 500 778 778 778 778 0 0 0 778 0 0 500 500 0 778 778 778 778 778 0 0 778 778 778 778 0 0 0 778 1000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] >> /F4 1 Tf npNM=(e&cntS33 (Dq&VW="bLppDR@3cZZc 0.470 0 Td (\)) Tj ET /F1 1 Tf ?/G480rQQ*iP5mZu '7iO=*W"[qr,$)N#f.o?=!DLWR1V?gY`Hkqmed U[KJ"7F(?_hP9>?2J`W\79n$KHZq">PnY9Z>A4J#YkO9Y&4jIl@EK9>Hl)(Hj/>5mSp'B>YGLhb+\WU RV*>!tL#O)CF4*@[`X_;UbGe_9Zd.mRhJ>*&jQZ-$^U*H@EA/8ubL9nU,X1&O,bP^7PP`OdnY+LXQOJ5mGNOA`P_.eqhipqhW("@'X`8 Tg_@nC@g*0&&r!s6Kjkh/8eU7.feQMki9dqd.`PDCA,]dKE!s[ Consider the following truth table: The table above describes the truth value possibilities for the statements \(p\) and \(\neg p\), or "not p". Tj :[Q^;I$N_jqiJRMWh;:l&QQ:O*t[\P!SnpS,.JmSbfjqOE3JL56B: Directions: Choose the best answer to the given questions or statements. Pigs can fly. 0.907 0 Td (equiv) Tj ET ET ;rCjmDh":idJTsb1tppft*3LR[-mnODZD&E-dA5CCI$&22LofWKHQKSVNTgT /Length3 532 201.6 442.56 m 202.005 442.56 l 202.005 456.51 l 201.6 456.51 l f 316.8 526.08 m 322.677 526.08 l 322.677 526.566 l 316.8 526.566 l f _1hiU*10L%i_S5Q9]YU3I*.ph7=q"7/'Hj3O2D(rF62lDk/_T:2dQ7SK?qeu>fQd.%mMSh%nF-XRe. nn+AN=kc:W-\k3RoOuZ*I(sb]/FO BT Nn@F:)Q$E$..r+>7GHFCfK6ARfgrDf-\:F`[t$F`8H`1a"GfDeEco@;K@iA0>i6F:)Q$E$..u+>7PL :r8Df"qCB>/3I1e2\RFP.=\YtP]Z6(0>ma,UBhXn0'P[_$bM7_.g-l9U9_am/C65LI1aMMVXk,StI0>?_hrYp`d@d:Lc"RSqm X&h?b)gPD/==D6a]qt$bk\iffQqdeQgXngdek=*7n/6Vt(3'YG[Hh)QPStl%)"!M^B?.RGPET[mp>G -28.628 -1.166 Td (prop) Tj /F1 1 Tf 0.836 0 Td (is) Tj 18 0 obj 4#W]@^u1[S45? )JIF`[t$F`8HX0Jst+BcqA;F:)Q$E$-kh2BXYf+E2IF$=n9u+>GQ/+>7LQE-670A9Di60ebR005MbM -c*De"tE/$X>bAt_j]52'EmJV[+-`g!T\PIjS+g4&$t!^6:m;^]!3Gshe=Q3`:p)Otq3Yq@`7Xk\=N[s1.oRFh"3e"T[8L_$,P:X[-l:Un?Ht72]GHGho^lMCXU -6m=(Gq! :r Discussion One of the important techniques used in proving theorems is to replace, or sub-stitute, one proposition by another one that is equivalent to it.
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