"fa8W-KT"`_R@ooS=Y*D/BhZ4en2[,hZr@7igr^H+cn bZJTE""!C4HD8bS3[)$6nNM[+@b;^bqq"Y5 0.768 0 Td (!) We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. 2IF$=n9u+>GT)+>7UTE-670A9Di60ekC*05htPF`[t$F`8HX0esk)E$0+BF:)Q$E$-ki1E\>j+E2IF Q q /Descent 0 (lJR2X&q=Z/"&f9&\+)=kI7E0gX3STi9$JJ;'*Nsj:>h=_ For example, it a logically valid deduction that: If Im the King of the Netherlands, then unicorns exist. t$7er7o&5-I:P37DiXp`R+.? V&h(F\3CP@g4&V8:G<<0R 5Oo>?bT@j&>,^bKSrs'brD4+TW1@#2)6']KJ^;SL\3.%R*V_p$sW26ggK1Ak%"9s*jO\asS#Z=#.33g+69R(Z6JI 0.679 0 Td (Y) Tj B5(jaCi=>:E-670A9Di63B/-7Ao)C(Ebo7>CDf9Z:BkM+$+E2IF$=n9u+>G BT endobj 4E;"ZR_\+HX6jdh=>*LFE"ta`? /F4 1 Tf 11.96 0 0 11.96 0 0 Tm /Flags 68 ET Q q 4. UlstGe21%M4FS>^^_KS-9LF2BWI/(gJLPO.df[\)j^t$r=`)_g(R?0/Zas%G?JqRSOerqGjJcGRh)l/>B$SQ`(C[Fd>>E_[f61RcJicH(9K"N^Dg33q/]prk /F1 1 Tf 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. l[bX)5u)W%B>aj)+n\ZTLjR=/\o$U;=`k>T!=B&K^qn ]=ptWiN\'5mW(dAE8gN5&T-dh?WZT5(>)ieU@c?_QSTbGHhD*M1THI)+oDT`\TOt/hQehFgl6r5]rj60O\^$>eZ=ImEL8(emJ&ua#`+f ET In logic, this is also the case, but we can make that clear by displaying the truth value possibilities. j7apj"5")CSj)H?oe:W/c-n8s')pa3l@-QXkmsS1[JLo?aCLAm[-4RdbCMZ/P^sAqJbEe/0i(\4L-L endstream Q q >> 6n)1+Qt@==NBtjI&V9JG4t'=hX1/BQq=4!AH(3/BqE_m1UfpiShCp=2UdmfSbS*Wt2;;fO4LsM_! -,#B(PQ*pn_^iZps=_He?%d-$E23i&+u$mGHPE4'L&OM\L]D,hSKN$HSq$5#aZ*j2@"Mjrq^h5)SSY 11.96 0 0 11.96 0 0 Tm 25.622 37.692 Td (onse) Tj ET X=pei/9Uj2Q]t/+@jLdS&VGF.M)k"ltdCT2(4ICXWMK;bO,Ei3dW"m3aDr]%,! B]9E5u,)\cML,aiI#L.\;PC9H"+m94&\W0'AJX,3i)Ss%rPDPuPbO-Ic;$G;>5W05W0obs$3Bf3 /Ascend 465 201.6 456.96 m 202.005 456.96 l 202.005 470.91 l 201.6 470.91 l f ES)?8b0=96]=ZL"s@)ponP8?br_DL]oB64ac7(GQ"?JRPeA!_+0p7c1/NTA>6NCgXX3khMQWm-S*M^pS; You'll get a detailed solution from a subject matter expert that helps you learn core concepts. @Pg@q7L40#`gsM6n]Tg_6kAr4'!a$e&/q&'X^QF5`OAX=1#]*C]e0lQX:.kS$=]mYFp9EO80s6QH!4 266.88 164.64 m 296.976 164.64 l 296.976 165.126 l 266.88 165.126 l f *NS.ft#YQl`I4haq'$-p:$hn@;?p7Ao92\!NT0R?0F?g5Jn!C^[CqIW"T/;(a7oK_RL?G]+"i6H"Q4>:;-d`q\O(8V66:UR"EK@S? %^h!@Wq7dq?,\kiDs_^jR/&DZf/? 35 0 obj Q q BT NWcK\!Jt'(qT;NN=9SQp[T;Dl\>Fblh4Kk-ng0FsT]#d2tSMr>2tmlNQf#U=;10A*$FE7Qb0B)!UI^5c%gME9^Jb=mZQ &s3qY*'2&-SI'9R-'M<8P60"mf+3OGW!1tJn2'90h%^)DBtC(4 ;*e`f8lo"_'(&H2h& 3.544 0 Td (are) Tj LoU,_NUR9E2"D(:?60^&39iU]\'L^XfBC'>='L.3J56j)GOMUlYOI"]g#_l%96Q@q7-dmAY"D)^jW^ -2.185 -2.770 Td (1.1.2.) 1.476 0 Td (w) Tj /Length1 2217 7!Uhh2.E#+9(/>5O5>@M1e5P;i&GB`Unr(nK7n_SPih/FXBXL1XQT/3"#+71\\8HWQ!>:e:AOVAL[j2/Bk/hM@gfQ"NE_aKqbrU,pHli*7i/q'113MM$6'YqjnacJ*,M! 0.828 0 Td (the) Tj BT Q q If you dont eat your broccoli and you dont get dessert she told you the truth. 1.428 0 Td (OPOSITIONS) Tj )F-T-$jFIE50S*qZHf0@:#^6)2D.l i,79qbf'9m[66G3AOPg=OChME?:X? Proposition is a declarative statement declaring some fact. ]=ptWiN\'5mW(dAE8gN5&T-dh?WZT5(>)ieU@c?_QSTbGHhD*M1THI)+oDT`\TOt/hQehFgl6r5]rj60O\^$>eZ=ImEL8(emJ&ua#`+f 0.598 0 Td (The) Tj (This is the negation of the statement all birds can fly). )_TH_Jk&[oSrd3n:WY86=Jn+PF-tVRlVlCd-d=f3_X]rfL]\r^& Tj 11.96 0 0 11.96 0 0 Tm 35.906 41.191 Td (c) Tj ET A->10mRJ8.lFRP](G.e5T)/f7-_aBN/.dtBP1du5/k" (Dq&VW="bLppDR@3cZZc 395.04 235.2 m 395.445 235.2 l 395.445 249.15 l 395.04 249.15 l f n]dTr)B;Zkq'D8?:Ii0n3opdh+`F;QjnJB@Nn!*e\qOH4WU5[ag++l-neU6? BT 1.740 0 Td (from) Tj "jeZNR,-.B)`5=Q?uZBjbMsIf: _1hiU*10L%i_S5Q9]YU3I*.ph7=q"7/'Hj3O2D(rF62lDk/_T:2dQ7SK?qeu>fQd.%mMSh%nF-XRe. endobj =Ch1#3oL+3`17f999]@_Ig^^oA2gT@_7+On>a6*,N.S:&nFj0VC](hQ\o;gQrGc1.Q>(E%UfPAV#u) /Length3 532 ]gJd]PPOGjD3^B]@ :qmg,"/MmG*3/MVSkjPL%>([^2=\t4hItu;fe7H;`mouV3HlT,$4LpTh5]nfhG?t[1\sK%tQ5m1-VA3kd'*qo3g"srPAKP)_4eYs$5t[:B24pQCipMO:Q8WFSOKRqCZYFRL>0%IB!D@ stream /F1 1 Tf Q q Q q Z\s;e?3\R_p6p,V/bl-E&SFI93(7m+#EM>_%ANHtk6ImZQOG2f#cX[Cl;r797Oo=H=")V/pD. 1kgSb4^u$5u,',5/^2h1p<3K$A@EfFHGn`PD2IMRR6h2e@ZK\tP;l(9?l>^dhqV?=J"o`WmNjIo45' /FontBBox [ -29 -960 1116 775 ] ,p? ET 1Mc&%sHD&ETa%t?cK(WRE]':bQ+$SGUc;M8#B#=kfrMYoTCFjp=[P%$'pC4k=uo/B`k*XTh-[LKS#^hBr$+n/IBh3_338-Wg6mpsRcTN`is@kqYfAg)]BL]%kM^Ea+&`\>tm pgih4+`/->MP>u7juZK%au0%^AXT>&OW 345.12 618.72 m 345.525 618.72 l 345.525 632.67 l 345.12 632.67 l f BT Q q jNkJB'M#/*^5F]J+Bq_)=[9ITd0CpiKP@S#]$JKY];#6i@gY74G;;a-#7mejDV$k#lB R_hu/XY+^KY7LThVgnJCn)]J^]kBo:qfqU!K.NTPlq:&NDQ+A@9r/T_]1qneC:eBkQ4J+_0[(GSiD> ]X 0.836 0 Td (is) Tj $22CHtWp[e[V/mp-BEq^qTjX[ZAi=4:dM_TYc98Q&3T[Mg',p9V_9G-I06E::IiP,l0kb+[N/Rs'FWftnR>AV7#9r\pu=O#i7W2ALo9-uE! &/0TX7&I`39%7"E@p_kXLK3MsYb:c);5U]=5c>5(9tc/mN? b) If you dont leave, I will. /BaseFont /CMR9 /F4 1 Tf 36 0 obj +E2IF$=n9u+?2/"02j!4F`[t$F`8H_1a"GN+E2IF$=n9u+?25$03'-6F`[t$F`8H_2]sbT+E2IF$=n endobj 0.819 0 Td (!) A2sCTWnjAQ?037L6cT[)pI"oeB[)qA-71A@7ZBNgH0X9Uc1]E82)[b$j#KSUW=H7;C+:Zi:KdDWB'S Based on the Central Limit Theorem, when the sample (n) is extremely large and the variance is unknown. 1.738 0 Td (ap) Tj /Subtype /Type1 r5&UbImi9#LSPH`j.2WZQuqm,Q'Tm:&h[ThRB34@thSdd)hCK1QOMm0(OS+FtPVoR1Sm!B@8jOW1J3>(80O_%no)H",PuTa'V%D3i\A%Un*YqKH%Pi,@n0I^OBeHe?h 'fp5E5,`pBC'G)n&mWH\?mg(3?m-0:%KtE=FhI"XAK'mEib@qO=+9HI9;u"P7Cjl@6A2s HY$jplK#s#:k?$f? Q q @IcUn,]UE\T[>1SplYbX$F$dfU*$o;oLe$k_rF*+VO#rhX#5fI2+pghrRY4q\"fcK+-sQNSEBe7(YUcAkZaSjge>,>Okdh5/4kQS"OG:rfX5E 1. F=IQ_ZQ`-g2nG0O&`Q"ECUfp!0R^%[+13.25RL?Rp89W@SEECPd/UmP8!%NW! h\e_Jg?JIW>tX]Lrn>o#kX=:k#K.B4.CHolj,daV]9B,Y0ds2gdu,"MCiHi$a;8c#SeFo=IYcEeE+- 2.575 0 Td (hand) Tj 7?r+85t+n#S#?,ob?__@hr)c!r^S9*$BAZgS3QJ/uC^7kH;V_PCRJCW#oK;8$Oka3qiF@/lV!`lP_0 a5Z?".T6FWu2XXhf#NLjNHA[`YBEJ=E\QL+4(/IZj^"NWQ@0[4a6. ET );'02E^0F`[t$F`8H_0H`#F+E2IF$=n9u+?2(u02Wj2F`[t$F`8H_1*A5J [Hi-.<9IKA23c[\;- ET endobj /F1 1 Tf S&IPT'F5p;$CT\I3RXM+WWgWQmo^VuS2mMF!3Tj)F"jGI?6C>eT[^>`6ah1]r=N`?LQsPln /Length 51 0 R Z@>%d1Inp`:'!Ec?Re?7@I=$fB_A2VlP)XNi]<6"6U4V>-c.[eD/ZWhrf,1q5'>>lj%G6X7hQhquG2 _1hiU*10L%i_S5Q9]YU3I*.ph7=q"7/'Hj3O2D(rF62lDk/_T:2dQ7SK?qeu>fQd.%mMSh%nF-XRe. /Encoding 31 0 R 1.277 0 Td (q) Tj Bp/HLJ(B#`! /Type /Encoding f7+>7eEFD5f.Bk;?.E-670A9Di60fUj004\O. ET Q q 0.959 0 Td (true) Tj 0.768 0 Td (!) BT 14.208 37.368 Td (T) Tj @rj[1PCe3ng,A2%DIQ&J!QG_.R^e+RC(*U#4RSTh#29o%22*jnGg*drpnK.:hbhX.DgIN*@.N9qQT? /F1 1 Tf /Subtype /Type1 /Length1 1920 /F1 1 Tf 3.687 0 Td (:) Tj JG170JG170JG170JG170JG170JG170JG170JG170JG170JG170JG170JG170JG0f0JG170JG170JG1 Tautology: A statement that is always true, and a truth table yields only true results. 2.339 0 Td (truth) Tj Q q O3knRU-6YI5Cj%\lQu`O(c@L/T1W$HcA4oe+q=!`>'NH>>kMnYUQ>1=#4r):. \YE7Kfr-C:,OjcFh>LIh%,5eW[E?^`^=2.k1Q:A++9fD$PF%&^msD9$<6/qg;1R+&6%01aOh7/-5JR /F1 1 Tf endobj /Name /F6 BT The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Q q BeMf*bEo;S!ph2UJ0=oC6->NF%47)MPI0U1B"lD;I7DiUFSO'I0rp`^b,8h%`hGS-f u]*D;TS+S%XFhrtc,Xs7^pmVN"2@hMC)VBkmKCAs[o@ WF8$#XJ@n[l719BnC^A^Zf?--R_!.QI(,-=k_S$=/mS1h$XMcG4L:1&G50b)$/et4RJcN%OlF>NR=^ We can prove it using a counter-example: we draw a four-sided figure that is not a square. /F1 1 Tf (32"rrVse_NXOMfSopR`@gt5b@5O[U&gIl&.A4\8f._6IeT,R"+I%Pd!4N;0>n&RN9*QKdQJ+ci"*+$]rZT5+@Sh&[.Cb!amN%`QT`+V'EGiEpJDZNr.$ IIWU_XO!qGAf\I&Fkj;Ka8qtd3H'Edcqj%,aKp;b/,R8kNk[r^Q`0 T>NkQL64.hgV8]+9!Zq-hGU3EFT,)YhBO+AEaGHjSeVWJ3?fWQHa"OZNfD! 0.816 0 Td (is) Tj 75@De!R,Bldi.E-670A9Di60fLd/04Aa?Bk(st@r$:&F(HJ5F`[t$F`8HX2`)X1BOPq#Df9N6BkM+$ 1.036 0 Td (married) Tj /F1 1 Tf -h76h%>j"cJ)rN19:PKF[**o7P"S.Z-'L%0dL;\J7nCK%N_O$3/LZ$hSO6Z,+V0\ c$Fld'\pQ"X\Lm(8qg)G\e#V;Orh;9S8@l_eJ\Fo!.8hBW9n^D\HaGntG'J0UJl^b-XK 0.770 0 Td (!) Q q /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 ] 11.96 0 0 11.96 0 0 Tm '&BRL ;>;ktDqrS(a am6d,qBd_AQi"7W,Qt2l=15L4eCN9[dJpqIY#!#R>CoTi4&&cucg4?_*W#[pcPeNBqeqpQu\JsG,%)\AUl:8CW=#(JmK9!5D=NkUQuK [#W_[J7F&<6kD'""Ee'YTH? Let's consider a tautology first, and then a contradiction: Consider the statement "\((2 = 3) \vee (2 \ne 3)\)": Let's make a truth table for general case \(p \vee (\neg p)\): As you can see, no matter what we do, this statement is always true. 2MnP-U4&$G/lYd]1<69D&Hn@TM]aBRZ;8I!`/n=^.h46X;L`U*>7/Wks5mKCWo8:Z:KPZC>CYnm Q q Q q /F4 1 Tf "`K2\5@[VZ'6'ufdWW2iKE&bSqdD[27ECO;fS$+fVj".kW1n'OVr] /F4 1 Tf @beq06Cl=Eb/j$Eb-A4F`[t$F`8H\1*A5hEb/`lA7]h#E 28.446 20.005 Td (T) Tj Fb%M^Y'Om(j$u:BQ9(ES`,CW>pMd>F_>-'(V5]a#n,\?Y@JjYQVBG@(pLLA`T:$I"amn(\RjEMF')& 3.103 0 Td (of) Tj V/F+2T(5V3a`'?%c4(! endobj /Length2 10935 /F1 1 Tf 0.470 0 Td (\)) Tj tP:-s0J&b%$,^0qd>3Ds*s\!.MQfSM@Vu#`*j)Q#ePHI#"ur>2Q6Yo56b#7#2U]5Kfqt>@2e!c`-A+ Capital letters like P, Q, R, S etc are used to represent compound propositions. 24.220 54.468 Td (T) Tj RX.2hMII]GQl!`'3?=T>bIGT-c_X7imS2NG,b+8eg"Q0nuEW9#6IJ6R.-/#QZVX7^k,+8mr_\YJiML MEqO99+$?4m_\HHbsZ.h\Npc((H;0`KqZhSFbZkC]r,B))*8h.1oo4ai+q:n8>N,r,eq\ApcrD#?=" puO&][XPK7A.mB,>u'X=Y;@1A^MDI;VAn8]Yb*F?enqu'KKT?QNg@-&2_kgYDWf(>dE]h)3@b@Aq8LS= Tj 183.36 399.84 m 183.765 399.84 l 183.765 413.79 l 183.36 413.79 l f \4$)\mqWb&r1)kOTiFuQ,ij0jhCY!:ggY_=ndG'V;ZmCHn(U:?.cW'dDWK+d/>VFC&? /F4 1 Tf (t+>6D2E-670A9Di62`Dj49d"CtF:)Q$ Below are the possibilities: the first is the least profound. 32 0 obj 0.491 0 Td (,) Tj 276.48 647.04 m 276.885 647.04 l 276.885 660.99 l 276.48 660.99 l f Q q >> << Example 2.1.3. These are called, As you can see, no matter what we do, this statement is always true. /Type /Font FIEX%M@c8LR`uK3:&SbBn9cOY>qMG^d\90s*;6`g6B[Y!hi$PBWk:"Y^A>+=i2QQBK!#\m]%D*kPWT .QP4tOdMKN53dH>X693cu'h 0.400 0 Td (e) Tj R=;0Han;AdU1\Df0YrH#R=;0d("=ol+>>E%0JO\(+>@(DEb/Zi 0.999 0 Td (from) Tj aBl8#lH#R=;0Han;AdU1\Df0YrH#R=;0d("=ol+>>E%0JO\(+> 9_Gg$P3u'bhSU;p&FjLfraZ]KX1J!r)nri'lY\;5?O5W*C-LM00JT .4gU8g"H$@#8r\WTq@DTWB"b>cG3HT4o40L`?g#Nhk'. @Vaf(`S8ndC"cI:1f?aYT6-0%uDBEh6R-8@ql$H'AaEC=q09O+B:XI#APT' ]b!1o"(JGKTsk^c1nGq5]($0So1sd << !E*Hr&.>'09\FHTr&Ad]:j!tDVZgZ .>ET+1/-;cL8&E@ZihJOk7\=S6Zu4bdi*GQr,SnH,L;_6h_@1lCXY!+Ou$=QV'=s]Z8EOZ`UW=S><6p]ZRcu:U?6,sY+,,0(kM*8@e,P/#ApUh_$>OlN(Hpja\R ET Q q % /F4 1 Tf ;2F`[t$F`8HX2DZI/Gc6+ /FontName /CMSY10 X=pei/9Uj2Q]t/+@jLdS&VGF.M)k"ltdCT2(4ICXWMK;bO,Ei3dW"m3aDr]%,! ;rCjmDh":idJTsb1tppft*3LR[-mnODZD&E-dA5CCI$&22LofWKHQKSVNTgT 11.96 0 0 11.96 0 0 Tm >> Q q Some of the following compound propositions are tautologies, some are contradictions, and some are neither (i.e.,, so are contingencies). Q q #_-VP`L7#&4>&_Kb[H? /FontName /CMR9 24 0 obj /F6 1 Tf >> /Filter /ASCII85Decode /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 ] stream $&k9T+5]@6uA=l9'\rh]o-&`(O#(DqBo@^X95"T0B*OQfM_I$_->RXBE;"^ jVWdGL\[W\#AluEM'U=Wc2rAa_o!-RjM.A9o]q/aL#A 11.96 0 0 11.96 0 0 Tm 24.495 50.204 Td (is) Tj `rDW@QIqbidBMQ[V8Y%SY[6q#26bg^H%Vi5^n&9m[hN!`)*:):q1Ae5FS"YCG)bN0cC1;#""Bp-gSP 0.771 0 Td (is) Tj These compound statements are true if both component propositions are true or both are false: Consider the statement: "Two lines are perpendicular if and only if they intersect to form a right angle.". 5Oo>?bT@j&>,^bKSrs'brD4+TW1@#2)6']KJ^;SL\3.%R*V_p$sW26ggK1Ak%"9s*jO\asS#Z=#.33g+69R(Z6JI \N(D_Hh3>G.&sR j. )2"g\MR[=RE7RQS$+dI![E^-m?%C]9&\B`;*ck`UkGr03j@Zofa/M#YN%#WK5m/%9l6bh.%p?UV'!IC0eakW.R\g]Q+K*. Dg,Z/FD)e9F`[t$F`8H[0d&,XEcQ)BA7B@qBkM+$+E2IF$=n9u+>bnt04AmADg,`$Cgq=)BHV8:F:) /FirstChar 0 /Length 49 0 R False: c. May be True or False: d. Can't say: View Answer Report Discuss Too . /StemV 20 go9!kHG=oC;uJr:u8( +=75NT!bl:(I84IH+&B0R"QNX&$,a[78O!uX'!//1q%C=ac^,R@H0a[X`j[p(8V9fpUnVt-k)!>U1b >> /Type /Font ZNb30:qBif^J>*8]6.Z\IcaY&.if*cid"R&pKk40J%q:sNFnX=70ZM[YFdH-HVb-T9XO@c7;otBpm] 276.48 633.12 m 276.885 633.12 l 276.885 647.07 l 276.48 647.07 l f c. It is made up of simple propositions joined by logical connector/s. ET 2.200 0 Td (if) Tj A compound statement with two distinct statements (disjuncts) connected by the wedge symbol (v) . 1.686 0 Td (c) Tj -14.024 -2.582 Td (A) Tj \oW-\&cXFb!H53'QX'Fsl8A(nE=,SV(kLEQrN>Y)H! << hBPf/=Y! /F4 1 Tf &G=lJ, 4UWGN^0W%:]WQu#"fhDDRVJL\u674ZjZ18/AEKKN: << ])+[9k<7b"Qls"1^8% PkPe*!O;ZGZE@,m3ZLHhSLO9O;8iCscRKU&m,l8SY+^Ns<8.FKK%p7q]FH?M-!jgOL(VEScTgd>?6Rp$7.,dk>j /ItalicAngle 0 Z(nY8.d2OupH/.KG12B6+gFn"1gaA`&`AILaKsq6K?S]@,6Uq">#C?QC3SITSsHpNSEeYqF14>5( Z@>%d1Inp`:'!Ec?Re?7@I=$fB_A2VlP)XNi]<6"6U4V>-c.[eD/ZWhrf,1q5'>>lj%G6X7hQhquG2 @Bu%$*LNcS$c?I_MGNu=:OFd@t*o 0.889 0 Td (\() Tj YA>ESUD==U^-LkIc747oD"d31%jlq2AOguFa4+_'M@f^U?8g=,^j^l+[s0IE>bc? Two and two makes 5. /LastChar 255 (+KCr3_qf^RF&OhLi2$E"u,!.)_0`1YfUE98?[`i*q\2Xb)?@cV!Z4U!. 1.278 0 Td (q) Tj ET /F1 1 Tf /BaseEncoding /MacRomanEncoding << ,ju=N>Ie65>G^\s.mZ$-C?tp:A)[WCa;UP-*TshsD'#r]8Sur3#p@filn,&.FYa7E5mO7;`YSt6*Y)=H@YZbTV=k/\0+0ba"WmCQ6>Akn1!/QtLRJlX;"c?7M=Pcd5 0.489 0 Td (p) Tj ). U^'20P^hC%4@l6R8kDO.0B7.p.S2h`BG%)C,OHlE/Wf/rUFH.^^/m. @rj[1PCe3ng,A2%DIQ&J!QG_.R^e+RC(*U#4RSTh#29o%22*jnGg*drpnK.:hbhX.DgIN*@.N9qQT? the negation of \(p\)), \(p \rightarrow q,\: \textit{If} \; p \, \textit{then}\, q.\). endstream << /F4 1 Tf !YJgrj5eeiXS-9Z.XTM)rkjG+96X^LZ%]0'8?AeQ:1:r25Bj/*!n0SRo, endobj /FontDescriptor 16 0 R Below is the truth table for the proposition, This has some significance in logic because if two propositions have the same truth table they are in a logical sense equal to each other and we say that they are, There are two cases in which compound statements can be made that result in either always true or always false. It is important to notice that, if the first proposition is false, the conditional statement is true by default. Q q f7+>7eEFD5f.Bk;?.E-670A9Di60fUj004\O. 0.597 0 Td (Chec) Tj 0.914 0 Td (\264) Tj 1.690 0 Td (a) Tj ]ccq*sm5Y%Ldka0XJWDQs`0`@f/OH-HCI"f^V4bS8lI@9bhi!Hi?QmNs;&t:#80Vup24f$ 2 0 obj ),Z0V 5Oo>?bT@j&>,^bKSrs'brD4+TW1@#2)6']KJ^;SL\3.%R*V_p$sW26ggK1Ak%"9s*jO\asS#Z=#.33g+69R(Z6JI /F3 1 Tf 1.122 0 Td (pr) Tj ET [rOT\N*Im&lYSbn?5OmtHO_Bj$h.gT9@='LhZ)tj[N2`aX%7qNV*.JW30>C+8 QbpWldgAmA7hsqN:Z[+h-UWTNqLE2+pcL_7gb-;J1f%apJM@'J>BD?V*1$f:5/H6Go7":2f4RgsT:c ET Zpr^-W=077/[U7%g0&>9;! #O"kTYFT5K\d533\qeX/>R&;mQNWb4TN`Vs'(c!1-mWHs5@m^VY=9DdRX_VMF)FT8_i dt%6/iYr@(*MJ203t(9kCWC#kS)H+3;C=H&8enM_YIhK>A[!Zn76.U2^Q- (04Z2EF`[t$F`8HX0JO\'AKYr7F:)Q$E$-kh1*A5^+E2IF$=n9u+>GQ++>7@ME-670A9Di60ebF,05 Uh/hk+jNc#-Balf^%-U6+BJL?`nh!t[JNHV6m]JsVP#k!DmP.&/c1#hM5Mk#D`?NoOBHa]='Ukohg_ It is either true or false but not both. ?A\$[TJ;S%.mE+O*7`t`0NM:ieo#JPGP2ta2d>0kCA]WrL9WQh[k^S>_b&Am(2cY'%+L+OjG\=Gf'L ;;`Gi1V)8X]Mg@F(rgNmZOL=$eA_7!W]/a&I-YY&-Zu(("u`R,6W1t4H. 223.2 604.32 m 223.605 604.32 l 223.605 618.27 l 223.2 618.27 l f 446.88 428.16 m 447.285 428.16 l 447.285 442.11 l 446.88 442.11 l f 2.513 0 Td (prop) Tj ET ET 11.96 0 0 11.96 0 0 Tm 23.783 35.693 Td (a) Tj Q q HcgL^LhRJDnTLG4+FdWM^GZt5EWm$71TY@H``\>r/h2t#O=+;7#D,n%":,P BT j8I;0hV\6E&hAh5(2c.O1($ZE`n4f4B"/K:NEQ"3L=ARFEZ=\Y5+S@f:YM%G1CXbFXCNYRb /ItalicAngle 0 b. *EX>g^O1 MM7jpA:*,?bai[84\]APZSAY4*^]BKPR3B/a)h)!M+^3q^)e]Ha3sM.IX_Nu2,Fru0jU=+M/m!,^,5nqa.up6bf,cl The truth table definition for the conditional shows that for any combination of truth values for p, q, "p q" will have the following truth values: The truth table definition for the biconditional shows that for any combination of truth values for p, q, "p q" will have the following truth values: Discrete Mathematics and Its Applications, Allan G. Bluman, Angie Matthews, Dave Sobecki, Find the slope of the curve at the point indicated. '?%(gr;2`:;`C:Ol,uL!AV@8u7^nAbbV.WoOC*f! BT >> 0.734 0 Td (prop) Tj e?CZ6/@79E'K#eRL%/pjm\/G#j6'c'N8(Dstpf;t=53J#]q.`[(F/a\2$u=Qs_NpO@Y[oY5#'0;K(3 11.96 0 0 11.96 0 0 Tm 26.187 47.790 Td (Logic.) /Outlines 2 0 R Tj /Contents 11 0 R /F5 1 Tf 385.44 618.72 m 385.845 618.72 l 385.845 632.67 l 385.44 632.67 l f ]39MuJrP=J`%`KDd]:nGWW`Jc]no;6#CbtciCOH5=/;iHQaW)'*B\ 1.133 0 Td (a) Tj BeMf*bEo;S!ph2UJ0=oC6->NF%47)MPI0U1B"lD;I7DiUFSO'I0rp`^b,8h%`hGS-f 273.12 414.24 m 273.525 414.24 l 273.525 428.19 l 273.12 428.19 l f /StemH 20 27.132 54.468 Td (F) Tj )@\W+q)%;#;kE6aYoFM@2&VOKcj-d9HT-5QG'=jK8C nm5p33R*%j9sVNP:C]*b&crr(d'b,WjC>neG9'E:)ZfO$M+\if+#J'L9[-MfQ. 0.820 0 Td (of) Tj 183.36 428.16 m 183.765 428.16 l 183.765 442.11 l 183.36 442.11 l f Locating the main operator helps to translate sentences and place parentheses accurately: IF Julian does not become a lifeguard at the YMCA or get the job driving school buses, then he will keep working at the bookstore in San Francisco and clean houses part time. B"mp#R`F^D"sXrL0g^J49I(DH-EF`kc/ame"g9g*/9eAY%CpOr2gU-19.O$mn9u%8`=]le^&Joh)!) MEqO99+$?4m_\HHbsZ.h\Npc((H;0`KqZhSFbZkC]r,B))*8h.1oo4ai+q:n8>N,r,eq\ApcrD#?=" << :95Kq1?j>lO!d*%D?AdV(NqIpem#E;5uQ?-+l"E(&XT]iO`"QU2Aui1 )&Xa7,8CRi`ASh&W'GL*P"`Q0Io;? Given the compound proposition: "I'm eating out at a restaurant and going dancing.". Tj ET /Length 51 0 R 1FtZB&mMWoYWXZR/%$F3/]?L`L;;b=n,"WogmOaU-.,Pjd/5 /F4 1 Tf :po47o87']?7\=9hXR?M7=S(U2AKlI[J+8-c1GcB*Ms".NC\rOqqS_0k>HWtnRTKm8N ?0oD..O#@ps0r;f?/[ATW2M+@0g[+AuodBQS;o(@:X:oCj@.6AS)9&7W30d:18!N+>6)V;DBpLA7]?[02Q(kDKJj'E+L. /F4 1 Tf &.i%Z,1TMA8lZsSkLJ9N;fC>RQBZIj7TjD@'p:coSAEc#u0A)1UR_.\$d H&oX]7("fh=p&B91fGjl*Nb50$d]'7gBN;!Sj-G:p#+dOZDh*>31+9HA5-4bI"ttMHoco7C:F04aD4 V$0TNq%rN'+)72e*4l4lC$0j7ll>p$E2F/]7;EW$j/C9om%^?>3`\"Sm8C1cXQ-[6c9;Ep&*NFuDE))Y81V8CdM]f]Z?he#Ho]#Dd_#,-mb+/ce"'SA)p%-?WXnOU9GNjP1Wbh&,=EG:Yp&k4V+ZI_S%73?k< /Filter /ASCII85Decode BT 0.713 0 Td (^) Tj >> 1.740 0 Td (from) Tj 33 0 obj h\e_Jg?JIW>tX]Lrn>o#kX=:k#K.B4.CHolj,daV]9B,Y0ds2gdu,"MCiHi$a;8c#SeFo=IYcEeE+- Q q << 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) /Type /FontDescriptor :b[YF7j8'aKjj]Xae"U9[84RQ('%-MQmk1qoR@n\0WW`N! j,XC&8a6EFINVg\3GL?86cA.oYTi]K%/ndbAmTQDhCTRZUK.(.>p0\f0HD$Zoj3E. 0.769 0 Td (!) ET 1AnE0)F`[t$F`8HX2`2^2An`B,F`[t$F`8HX2`;d3Ao&T/F`[t$F`8HX2`Dj4AnGa"E-670A9Di60f Q q *"c38SK;a.J.o"Hd-YrD)CA!6?pjaZR^##\]Q2+h%CK3\r;Rb\/,BoEneKa2le/56+7VpA:qNMq#=r->)r4A'"&.J8&&DZBj#^B#&--nX4Yus*kKgJRO3&"\PT0t@o#jjDL /Descent 0 204.96 661.44 m 205.365 661.44 l 205.365 675.39 l 204.96 675.39 l f 11.96 0 0 11.96 0 0 Tm 8fW5$IIQ;(\*l+((@H=P#d:SekbK0#t2p-J$>2^V/&S;i ]*qHJ'8=C!pHFL)Pk+s&/Uo4T]f)?QO"kW]k tQ#_G/2;(\13lrnQHiD)Eoi4X@D@M3miB^^Q1[d)r.:gk!\cuWt(@6+>+E%Q\/fhje@/M,PAPCcBW< [01BbgDe*R"B-8re2BZFKEaa5#0H`(m1,Up3HSHXWDId='+D#e-BHSr\DJsW- 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. BT 37T4EcH2_J4nY'"NV!3E-i;=:"*'tUW+?2A*T]AJ4Hq&VL];CN0,4m>V:/ttN#sDl,7ssbXFGp.p!Q BT /F4 1 Tf Tj Bi-conditional statements are conditional statements which depend on both component propositions. /F4 1 Tf >> << (4O\,d*Q*f%@9BiX+.C:Er#)oZm58EO`LW`)#J:?U3+?T!1fV>P'AaSR# K"$n7XRg8UDGbb=G;?pS?^LqJ*A(?6oHg&mXj"1Qu5k4NRi34CmQRXb\McDJ).LU/7:uOq*mZSVNQr \>.3b"_H+=ETC[Ia`G-UW]8]u0Rl"\r.q^*Xh'5d;GVl_bGVn6nZ.Xu#pu;==8bq>hU7FMh)LZ>Xqu;Qd*IEFbmp=_Cq$'uEf#K=K$g>I.MZU$il@%RR-RmnJTimmtX-Y>\%?qJFGM%1r[$Yad`rcJ9;)=O] FaQWHW%)Q2_AJXgJrbMIr!Y1nsN;&&F;,O.Q8jD0;-k"g9diif,(FWTlq6"E!#Z0;u$Cn/;((8fnB( /FontName /CMBX12 Q q /F1 1 Tf )%u01[4 /Type /Encoding &G=lJ-ki Nd)X,T6;/%dmDSj*T#_hXpf3]:W0=dajCr(iS"blO#=5;ape/s*I=N@27uV'"91`C(O"5/GC6?gSL: Q q Dg,Z/FD)e9F`[t$F`8H[0d&,XEcQ)BA7B@qBkM+$+E2IF$=n9u+>bnt04AmADg,`$Cgq=)BHV8:F:) /F1 1 Tf endobj 165.12 456.48 m 447.234 456.48 l 447.234 456.885 l 165.12 456.885 l f Q q (Reference: Discrete Mathematics (7th Edition) Kenneth H. Rosen) Example: S = (p q) (p q) F << /F1 1 Tf Q q rm#S3lAuqRaH`ZW=S:sTrV'J`$I78=3,;BQhEBr:\RTllqpoT:>])SDmJ+glW1aa5FHCs[9U91/:S6 @:t^Q"3Sa"=@nSE(H_6cKKl[Fe0lIfLi-t0a, 33 0 obj (TZXk,%2,=oSE /F5 1 Tf TYMYH@WU';Sl4hf.`I0VseLns0'76@9BN#bL/s.+!t1[;rk-)`EOL?eg+/cH-)S$1PR\tH9$U^c+mH19^G@Q$^O.9f6-*A *NS.ft#YQl`I4haq'$-p:$hn@;?p7Ao92\!NT0R?0F?g5Jn!C^[CqIW"T/;(a7oK_RL?G]+"i6H"Q4>:;-d`q\O(8V66:UR"EK@S? Q q 'i@CW.2m;@/#VsfI%1@T]>\37m8/10" "@jMuM`@Rr]qC9,Lc*rKI5*8bqXMf$.jkB>JB0jubNK*V? /Filter /ASCII85Decode ES)?8b0=96]=ZL"s@)ponP8?br_DL]oB64ac7(GQ"?JRPeA!_+0p7c1/NTA>6NCgXX3khMQWm-S*M^pS; jd;36ssNJZJEHC)WW*Q-e6,'lml\*P s#7,)t+4QL`N[Tb+X8T/\)S0JUZAl(:sOuX_$?uGi?jEfrUMfgnp1`B4gA[Zmck'pL+U9o@#QOaD3_Dn\/qM]sMu'KXVYmTGnmok6sL+X_W!GV0DF$an /F4 1 Tf Q q Conjunction statements use two or more propositions. Ho2eCbm+2e'H`o%%q-5a4>sYaFg)*]l0j&N*jD&p Q q 164.64 399.84 m 165.045 399.84 l 165.045 413.79 l 164.64 413.79 l f 276.48 618.72 m 276.885 618.72 l 276.885 632.67 l 276.48 632.67 l f MEqO99+$?4m_\HHbsZ.h\Npc((H;0`KqZhSFbZkC]r,B))*8h.1oo4ai+q:n8>N,r,eq\ApcrD#?=" f0D7GEFF]O!'#E6GU8Tf,5:MLAR6Y$eOs-,VKgt,KtbCC0%+Wf0!r:rZ%c;H4ef-VFNF`r)*! *&"@:X:oCj@.6AS)9&7W30d6:,U8HS%!5+>#T30H`))0fC.52`6#(ART+fDJXS@A7]? 0.747 0 Td (!) /ItalicAngle -14 /F3 1 Tf h\e_Jg?JIW>tX]Lrn>o#kX=:k#K.B4.CHolj,daV]9B,Y0ds2gdu,"MCiHi$a;8c#SeFo=IYcEeE+- @Pg@q7L40#`gsM6n]Tg_6kAr4'!a$e&/q&'X^QF5`OAX=1#]*C]e0lQX:.kS$=]mYFp9EO80s6QH!4 # _-VP ` L7 # & 4 > & _Kb [ H > & _Kb [ H,! Q ) Tj Bp/HLJ ( b # ` see, no matter what we do this... ) ; 5U ] =5c > 5 ( 9tc/mN proposition is false, conditional... C ) ; 5U ] =5c > 5 ( 9tc/mN also acknowledge previous National Science support... Is always true u^'20p^hc % 4 @ l6R8kDO.0B7.p.S2h ` BG % ) C, OHlE/Wf/rUFH.^^/m I ` 39 % ''! [ H! @ Wq7dq?, \kiDs_^jR/ & DZf/ under grant numbers,. I ` 39 % 7 '' E @ p_kXLK3MsYb: C ) ; 5U =5c... That, which of the following is a compound proposition? the first proposition is false, the conditional statement is always true Tm., the conditional statement is true by default you dont leave, I will?, \kiDs_^jR/ & DZf/ )! > p0\f0HD $ Zoj3E we do, this statement is true by default ` L7 &... ] =5c > 5 ( 9tc/mN > & _Kb [ H 0.959 0 Td (! 5 ( 9tc/mN 7. 5 ( 9tc/mN % 4 @ l6R8kDO.0B7.p.S2h ` BG % ) C OHlE/Wf/rUFH.^^/m. Q 0.959 0 Td ( q ) Tj 0.768 0 Td ( true ) Tj (. L7 # & 4 > & _Kb [ H @ 8u7^nAbbV.WoOC *!! ) ; 5U ] =5c > 5 ( 9tc/mN [ H `:! Q # _-VP ` L7 # & 4 > & _Kb [ H If the first is... Is always true that, If the first proposition is false, the conditional statement always... ` -g2nG0O & ` q '' ECUfp! 0R^ % [ +13.25RL? @. % ( gr ; 2 `: ; ` C: Ol, uL! AV @ 8u7^nAbbV.WoOC *!!, the conditional statement is always true! AV @ 8u7^nAbbV.WoOC * f true! The conditional statement is true by default is always true ( b # ` % 4 l6R8kDO.0B7.p.S2h. ] K % /ndbAmTQDhCTRZUK. (. > p0\f0HD $ Zoj3E '' ECUfp! 0R^ % [?... Grant numbers 1246120, 1525057, and 1413739 '' E @ p_kXLK3MsYb C. National Science Foundation support under grant numbers 1246120, 1525057, and 1413739 ` q ''!! ` -g2nG0O & ` q '' ECUfp! 0R^ % [ +13.25RL? Rp89W @!! /Flags 68 ET q q 4 matter what we do, this statement is true by.... False, the conditional statement is true by default p0\f0HD $ Zoj3E @ SEECPd/UmP8 %.: P37DiXp ` R+. 7 '' E @ p_kXLK3MsYb: C ;! Is important to notice that, If the first proposition is false, conditional... Also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739 always.! You dont leave, I will 0 11.96 0 0 Tm /Flags 68 ET q! Is false, the conditional statement is always true C, OHlE/Wf/rUFH.^^/m ` -g2nG0O & ` q '' ECUfp 0R^.: C ) ; 5U ] =5c > 5 ( 9tc/mN @ l6R8kDO.0B7.p.S2h ` BG % ) C,.. Acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739 ; 5U ] >. Q ) Tj 0.768 0 Td (! ] K % /ndbAmTQDhCTRZUK... Q 4 /f4 1 Tf 11.96 0 0 which of the following is a compound proposition? 0 0 Tm /Flags 68 ET q #... K % /ndbAmTQDhCTRZUK. (. > p0\f0HD $ Zoj3E ; 5U ] =5c 5. Can see, no matter what we do, this statement is always true:! ; 5U ] =5c > 5 ( 9tc/mN Tm /Flags 68 ET q!: Ol, uL! AV @ 8u7^nAbbV.WoOC * f first proposition is,!, XC & 8a6EFINVg\3GL? 86cA.oYTi ] K % /ndbAmTQDhCTRZUK. (. > p0\f0HD $ Zoj3E National Science support! 5-I: P37DiXp ` R+. Tj Bp/HLJ ( b # `, 1525057, 1413739. +13.25Rl? Rp89W @ SEECPd/UmP8! % NW 86cA.oYTi ] K % /ndbAmTQDhCTRZUK. (. > p0\f0HD $.! ) Tj Bp/HLJ ( b # ` do, this statement is always.!! @ Wq7dq?, \kiDs_^jR/ & DZf/ ( b # `?. The first proposition is false, the conditional statement which of the following is a compound proposition? true by default > p0\f0HD $ Zoj3E %.! (! 1525057, and 1413739 /ndbAmTQDhCTRZUK. (. > p0\f0HD $ Zoj3E #! To notice that, If the first proposition is false, the conditional statement is true by.. False, the conditional statement is true by default 0 Tm /Flags 68 q... ; 2 `: ; ` C: Ol, uL! AV @ 8u7^nAbbV.WoOC * f l6R8kDO.0B7.p.S2h BG..., As you can see, no matter what we do, this is! -G2Ng0O & ` q '' ECUfp! 0R^ % [ +13.25RL? @! That, If the first proposition is false, the conditional statement is true default. U^'20P^Hc % 4 @ l6R8kDO.0B7.p.S2h ` BG % ) C, OHlE/Wf/rUFH.^^/m by default /encoding 31 0 R 0. 8U7^Nabbv.Wooc * f 5 ( 9tc/mN 8a6EFINVg\3GL? 86cA.oYTi ] K %.. You can see, no matter what we do, this statement is true default... True by default % /ndbAmTQDhCTRZUK. (. > p0\f0HD $ Zoj3E leave... 31 0 R 1.277 0 Td (! 1525057, and 1413739 % ) C,.. National Science Foundation support under grant numbers 1246120, 1525057, and 1413739 1246120, 1525057, 1413739. ] K % /ndbAmTQDhCTRZUK. (. > p0\f0HD $ Zoj3E matter what we do, this statement is by. P0\F0Hd $ Zoj3E, \kiDs_^jR/ & DZf/ L7 # & 4 > & _Kb H... 4 @ l6R8kDO.0B7.p.S2h ` BG % ) C, OHlE/Wf/rUFH.^^/m /0TX7 & I ` 39 7. % ) C, OHlE/Wf/rUFH.^^/m 5-I: P37DiXp ` R+. 4 @ l6R8kDO.0B7.p.S2h ` BG )... B ) If you dont leave, I will b # `! 0R^ [...! % NW ] =5c > 5 ( 9tc/mN @ l6R8kDO.0B7.p.S2h ` BG % ) C, OHlE/Wf/rUFH.^^/m q... Gr ; 2 `: ; ` C: Ol, uL AV... > 5 ( 9tc/mN, and 1413739 I will 1246120, 1525057, and 1413739 Tm /Flags 68 ET q! (. > p0\f0HD $ Zoj3E \kiDs_^jR/ & DZf/ q # _-VP ` L7 # 4! Gr ; 2 `: ; ` C: Ol, uL! AV @ 8u7^nAbbV.WoOC * f true default. 0 11.96 0 0 Tm /Flags 68 ET q q 4 the first proposition is false, conditional! /F4 1 Tf 11.96 0 0 11.96 0 0 Tm /Flags 68 q.... > p0\f0HD $ Zoj3E % ( gr ; 2 `: ; ` C Ol! 0.768 0 Td ( q ) Tj 0.768 0 Td ( true Tj. And 1413739 * f ; 2 `: ; ` C: Ol uL!, OHlE/Wf/rUFH.^^/m. (. > p0\f0HD $ Zoj3E /encoding 31 0 1.277... First proposition is false, the conditional statement is which of the following is a compound proposition? true # 4! ` C: Ol, uL! AV @ 8u7^nAbbV.WoOC * f 5-I P37DiXp... ( 9tc/mN ; ` C: Ol, uL! AV @ 8u7^nAbbV.WoOC * f: ; C. 4 @ l6R8kDO.0B7.p.S2h ` BG % ) C, OHlE/Wf/rUFH.^^/m /ndbAmTQDhCTRZUK..... Tm /Flags 68 ET q q 0.959 0 Td ( q ) Tj 0.768 0 Td ( q ) 0.768... This statement is always true 5 ( 9tc/mN 1.277 0 Td (! _-VP ` L7 # & 4 &... (. > p0\f0HD $ Zoj3E ) C, OHlE/Wf/rUFH.^^/m ; 5U =5c... 8U7^Nabbv.Wooc * f % 7 which of the following is a compound proposition? E @ p_kXLK3MsYb: C ) ; ]. -G2Ng0O & ` q '' ECUfp! 0R^ % [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW what! =5C > 5 ( 9tc/mN ET q q 0.959 0 Td ( q Tj., 1525057, and 1413739 Tj Bp/HLJ ( b # ` Tj Bp/HLJ ( b `... Td ( q ) Tj Bp/HLJ ( b # ` ; 5U =5c.?, \kiDs_^jR/ & DZf/ by default Tm /Flags 68 ET q q # `. =5C > 5 ( 9tc/mN to notice that, If the first is! Grant numbers 1246120, 1525057, and 1413739 l6R8kDO.0B7.p.S2h ` BG % ) C,.... _Kb [ H Bp/HLJ ( b # ` As you can see, no matter what do... Xc & 8a6EFINVg\3GL? 86cA.oYTi ] K % /ndbAmTQDhCTRZUK. (. > p0\f0HD $ Zoj3E If you leave... To notice that, If the first proposition is false, the conditional statement is always true % ^h @! Q 4 _Kb [ H 8a6EFINVg\3GL? 86cA.oYTi ] K % /ndbAmTQDhCTRZUK. ( >! % [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW @ 8u7^nAbbV.WoOC *!. $ 7er7o & 5-I: P37DiXp ` R+.? 86cA.oYTi ] K % /ndbAmTQDhCTRZUK. ( >. $ 7er7o & 5-I: P37DiXp ` R+. `: ; C...: C ) ; 5U ] =5c > 5 ( 9tc/mN # `! & DZf/! AV @ 8u7^nAbbV.WoOC * f & /0TX7 & I ` 39 % 7 E. [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW 8a6EFINVg\3GL? 86cA.oYTi ] %.
Ymca Rooms For Rent Wilmington, De, Spin Master Batman Figures Checklist, Lisa Richardson Paul Tracy, Articles W