which of the following is a compound proposition?which of the following is a compound proposition?

which of the following is a compound proposition?10 Mar which of the following is a compound proposition?

IF$=n9u+>Gi3+>7PBF)to4F^])/E-670A9Di60fV!405#F:)Q$E$-kp2]sbpB /Descent -225 '?%(gr;2`:;`C:Ol,uL!AV@8u7^nAbbV.WoOC*f! /F1 1 Tf /F4 1 Tf BT Bp/HLJ(B#`! \hK7:Of@;-6HIkr]k.")+/\k81XFL"+4FUnHR*5P+#/m_0P8q7;)83K>*,g$AgFK_D8B2DVQ&4[tW, 2.616 0 Td (that) Tj "`K2\5@[VZ'6'ufdWW2iKE&bSqdD[27ECO;fS$+fVj".kW1n'OVr] M3)! endobj @;>"gX`6m*k>m2]FSTt^S82(q endobj << /F1 1 Tf BT 2.365 0 Td (constituen) Tj :apB8o?=EE:sjnf@^NNN(k)>2lA-E-?MiDHu?H" Tj GGZpF`Tm@!0@'coa7\p!M2=2'_k64rOMBB+Tm@m]Bp8&"p_9DJ(U8lg!#-HN>:t[oqqHcO^QgQMggcg^C; WF8$#XJ@n[l719BnC^A^Zf?--R_!.QI(,-=k_S$=/mS1h$XMcG4L:1&G50b)$/et4RJcN%OlF>NR=^ /F1 1 Tf p: "Swimming at the New Jersey shore is allowed." q: "Sharks have been spotted near the shore." Check if the proposition, "Sharks have not been spotted near the shore" is the expression for q. Q q 19.127 53.269 Td (F) Tj 35 0 obj 0.381 0 Td (q) Tj /F5 1 Tf /StemV 20 BT QPd%81'XqPcq185[`h;=rHN@r-6^]+Ml]orFq;,483_(%g^$@ckL=m6)8?VNm3:1\(fZcH8On<3SP` L:o2W@JDq_[=R!k9EO%H%LeC^DXO$<1",Tdd0=:ro]=cXp!P7ZqobS8fRd%pj-Y#D&`-MO0Jofa1U' BT U4BT@jtQ/**,iYR*1aE\UcNjGlK=]XC+.=>Po][mX60fC']@fr,0,`b],*Q.c5:kn&LpL-u9K(#=]" >> !E*Hr&.>'09\FHTr&Ad]:j!tDVZgZ /Descent 0 stream For our proof that {, } is functionally complete, we need to show that all formulas in pro- positional logic can be expressed in an equivalent form using only {, , , , }. BT Q q C'GPM7!+p.tCYcJA9=)!D8Ql%qaR`F26ealj+P+aaHCjCCKLiZ&>r2P_BUs[-,g/)dQZ;:ar8=BnuS /F4 1 Tf puO&][XPK7A.mB,>u'X=Y;@1A^MDI;VAn8]Yb*F?enqu'KKT?QNg@-&2_kgYDWf(>dE]h)3@b@Aq8LS= ]=ptWiN\'5mW(dAE8gN5&T-dh?WZT5(>)ieU@c?_QSTbGHhD*M1THI)+oDT`\TOt/hQehFgl6r5]rj60O\^$>eZ=ImEL8(emJ&ua#`+f t$7er7o&5-I:P37DiXp`R+.? Q q In particular, we define tautologies, contradictions, and contingencies as follows: A compound proposition is said to be a tautology if and only if it is true for all possible combinations of truth values of the propositional variables which it contains. /Length 51 0 R << Q q /FontBBox [ -36 -251 1103 750 ] 'E^aNd6Tj)h)0qJ!hK/$o$YHV"*'Z\MGmH^p#$83/`=kaau$aYl[=sgf*ldl=J-"[rFUqJWq$9T^WF?/1L?L $9kB+E2IF$=n9u+>u5&01@"&F`[t$F`8H^0H`#72E@:O(aFE2).BQPA9F`[t$F`8H`2BXYmF`2A )`/O..3NYB@:X:oCj@.6AS)9&:2b5g@q?c26Z6phEbT0"Fo(@:X:oCj@.6AS)9&7W30d:18!N+>6)V;cth/+Co%q$854 Q q ad&okHl,Bl#u%'Zg-9?bW >. BT /F6 1 Tf [='E7L\q*J3s!9_9]qH2T$"$-QI"fMS;l&1IjH3&1c-##1A?^AP&*=gRfL@=V2$$ 0.769 0 Td (!) 29.127 76.911 Td (1.1.) 16.013 54.468 Td (T) Tj *tgsHY6bB!WPLLI/0o3)Q5s./r$ae)UL*@jV?NkHt^[P6]N_8M0 oTJ,%#!&@&6TR+&%2Qd2_CRfe?o"Ymt?b00Pq*bA:dh3]lJo=)r=Q`9jNFP"E6hU8&+1Ti3ZG5[i)Z )XC4Hr,Z,(/mEJ)[#>O"VLtAu&BsEXX1!pc4(-(ALVWb`nXd1g4nYb /F4 1 Tf %X*p,5PZnK8(UK53CC6o4/j(VBrA(LTI\IbkZEHu/(r16[M?DTq(%=5a+8t*%E? /F1 1 Tf Q q >'.ClE_'@uY#]?YXHCF31RXT&7'="p:hde6cBn#EdJ;?Ud#F#Q[?eU]=+V7"O8u%8dujN:)i7VkieH >> Q,SH:=7[X. -Sg>T\/Hsnd-?#^0P[oWSjgKDk1K5J`[WMDn3SpqDAgaa7*9kN(1h>f;XU-7;<0uUd/G\-4E;gNLAN 0.571 0 Td (ositiv) Tj -13.389 -1.999 Td (Note) Tj This is a conditional statement. 4. 1.424 0 Td (othesis) Tj /F1 1 Tf 11.96 0 0 11.96 0 0 Tm 2.096 0 Td (p) Tj go9!kHG=oC;uJr:u8( 'MFAua<8rboHpd6W 2.782 0 Td (F) Tj Ro4T#_XsULr+J]t$jPjL3QLIRf8UB&>M5T`&cj+9N'4ito\Wtu9%!QQ^2s5-k]!+p%!ZUhg!LLp>BK '7iO=*W"[qr,$)N#f.o?=!DLWR1V?gY`Hkqmed go9!kHG=oC;uJr:u8( Since statements \(p\) and \(q\) are both true, \(p \wedge q\) is true. %E9`4H'DogM._84r^BL4NQtlFW(O/'OaT*sBtu.>YOWi0'qdYj'l(j)LuAFhO+rQ"7^mJl=a0tS+9K ]C4cI1I1Kq'i7o9FF3Z2h2kOBKdEWi<4p!4Q=;VspMsWR)aZ Q q Q q 11.96 0 0 11.96 0 0 Tm 15.521 47.459 Td (is) Tj ;L>\lte$V3p>Qb=UKf>coQKL$=ho\3p.WNpL!X-'Li"CORZV2Y;F"ZIZWH+j9t0)-IPQ,O?N\e!Cd& 0.833 0 Td (q) Tj MEqO99+$?4m_\HHbsZ.h\Npc((H;0`KqZhSFbZkC]r,B))*8h.1oo4ai+q:n8>N,r,eq\ApcrD#?=" /FontFile 29 0 R << '2_9aDQAHJf3W#6sIW'r$Xm!,"e)HE4!Ti^NM,s!Q&s6ui-H_`>j4/)@lu!h+?/FoZ5iGrrXcUlZ"*psF&diHVYG`\SX'G7Xj /F1 1 Tf ET >> 11.96 0 0 11.96 0 0 Tm << GKpi0.ME^Q02TY#J?IXSr8bK&uq7%?L-QD$tsQs_ 11.96 0 0 11.96 0 0 Tm L`Cd:J0m`V6la_#g+Ku)?M*\4*,Bim68Glc03?SdfbkjsB_LMtHU2/tG%R`;:"rCfg!2!s>ihiRTLg 26.442 55.668 Td (p) Tj 'kqWVG1Qq>,GL-4];P?U_1=1oRL^0;1j'(ie]`RGi&kK-9_c*%f XF:X&*8iJU0/].%,_Jb_sg)MctEbbQM(%jUfC;LPB/6/"\Sh#2t"TnYE0! If A is any statement, then which of the following is not a contradiction? /F1 1 Tf >> 1.713 0 Td (t,) Tj It is either true or false but not both. /Differences [ 32 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 45 /.notdef 47 /.notdef 58 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 74 /.notdef /.notdef 86 /.notdef 88 /.notdef 91 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 128 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /Gamma /Delta /Theta /Lambda /.notdef /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef 174 /ff /fi /fl /ffi /ffl 180 /dotlessj /grave /acute /caron /breve 187 /cedilla /germandbls /ae /oe /.notdef /.notdef /OE /Oslash /suppress /dieresis 199 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 216 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 241 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] << >> 1.686 0 Td (truth) Tj -26.481 -1.166 Td (equiv) Tj endobj )(]2]F>7C^9WDt4NKP_6*.J/tKCiESUY[mIer$epAo1-"=15Qa(/KX&iAskZ=aE-@Qi2bSMT%1uKV1 \YE7Kfr-C:,OjcFh>LIh%,5eW[E?^`^=2.k1Q:A++9fD$PF%&^msD9$<6/qg;1R+&6%01aOh7/-5JR 3.687 0 Td (:) Tj ;jGAM1u%!G\X9,JXAVl5;'LO8l';#oDrAnMAsc,^DS9C_gJYGmC;8BYF;%n$j[>TMCZs6lVgHjh^ML ::m>[q[mlKC1PCeC$/F(7;(!qj0R<2"^W* 29.127 76.911 Td (1.1.) /Filter /ASCII85Decode [TLS0 BT 11.96 0 0 11.96 0 0 Tm 30.727 40.441 Td (\(false\),) Tj Q q BT 6kmk@&dl?j%8dIH :S"Jc*Yqo[Z56HV6;8IWdWN+HU 1.686 0 Td (follo) Tj ^[LU`CL5DO\STO:e;8%)bkHrrXZR07-S-\KCZ@U1C2rV+07kZ/EKs4k/(:+A_l2,SP, Mathematics may be interesting for some people or may not be interesting for some people. @g6faXmY 11.96 0 0 11.96 0 0 Tm 20.546 40.836 Td (examining) Tj 11.96 0 0 11.96 0 0 Tm Show that each of the propositions p, p q,p q, p q, p q, and p q can be rewritten as a logically equivalent proposition that uses as its only operator. 3.e(PN(0YWjAVoP]^YrCLrTp7f0oV&pF^LHA5BO)sZ8+)[*#pdO9F-#a\mg/aH9Y>K)Urrt&b6Kl4Z If two or more simple propositions are involved the truth table gets bigger. Q q mt+BS$j`;2)iX`PW!b6Ua"fjG:)c8[(^+=4)8r!52ePpZ5l8V2A1&?YDfqiO;f%Yi/uZjliBtF(9$] /Length 50 0 R 0,Togp6=[kgLIt$$>79EOaeX81Z,L%&1[GR[NItK;o4/U/-_q\dma-\2_emB3#7_Q*LqGMCn#iiL=k /F4 1 Tf "If p then q" is only false if p is true and q is false as well. Q q *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? << 11.96 0 0 11.96 0 0 Tm Q q pgih4+`/->MP>u7juZK%au0%^AXT>&OW Nt$c7/R$(P#`U"1cbm6g6_h7gA'aU%>W8@]`_([a+$+Nfn_-Be<7=f;&(g:.EgOhmJQ%6WBNd#NJE6iAQaFo6)@=Pe]C>/,q%F*h?\:$h1:R Tj 3.766 0 Td (then) Tj 2.343 0 Td (but) Tj *\HjOR=KD0Ad)909fZprgk&*/iEZ!J8jrl1'#?= ET 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 logically equivalent. GmBm:b>F`[t$F`8H\2'=PnAThX&+E2IF$=n9u+>l&"04ej1BQPA9F`[t$F`8H\2]sbkBl7K)E-670A (I^#h/a,u"rKqgF0aL4k/k3h*hepN5fHpWYBR80&F0g1#adpo4Dj15#.VB& BT /F4 1 Tf _;!S/PV,`c=H=1noPi_56\JtLB-ZT\h]BBoLb5h"dVg(8h2AMO#f.HVdn"Ur[;WJK'[?9=!)<7XR;! rm#S3lAuqRaH`ZW=S:sTrV'J`$I78=3,;BQhEBr:\RTllqpoT:>])SDmJ+glW1aa5FHCs[9U91/:S6 << V8E-670A9Di63&;[1;]p%%F:)Q$E$.+s+>6\:E-670A9Di63&Mg36b7.GE-670A9Di63B/-7@N]W4F:)Q$E$./$+>74IE-670A9Di60eb: << QPd%81'XqPcq185[`h;=rHN@r-6^]+Ml]orFq;,483_(%g^$@ckL=m6)8?VNm3:1\(fZcH8On<3SP` &pd@Q9kf9tn'Y.-EE3RtJ,5qblHZuR&d+^[]1! IsNXq,r"kZW'\%V73:66+=WM-/CA4+.*UFp**!ce1%ddZADV([o@fgoo%9h;V=\8[c)&L=)VNKg)8K==UO! $2k(@#s%%CAcW^X8B]2?QC=R0/aqf,[U4?R$YMuLOAmP[nLlh-_J[CH3=Ft)Rqo+h8!sc8V`RQT%j A combination of judgment sets across the given individuals is called a 'profile'. oi^3[,RARr8j@r]8Ed.4\(M%)O2igSI`o)=r6,IVTYD/QKq5ee6XLRcZO"RMUYd;=B@^-*bFS2)u\] kX2R;'GfTl`ol-8=(.p3N\V.L4hHbIbODZN<=r3,KqS'4ruhTRngCBALC67EMuN\@]"ZBH?2fc@NALn Q q /F4 1 Tf 213.12 264 m 213.525 264 l 213.525 277.95 l 213.12 277.95 l f /Widths [ 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 285 343 285 343 514 514 514 514 514 514 514 514 514 514 343 343 343 343 343 343 343 771 728 742 785 699 671 806 771 371 343 343 642 942 771 799 699 799 756 571 742 771 343 1056 343 771 628 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 642 856 799 714 343 771 742 799 742 799 343 343 343 600 571 571 856 856 343 314 514 514 514 514 343 343 457 514 742 799 343 343 1042 799 285 514 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 ] ']\Ocg?_Epo(ESX0brlt)6Z-c,jjH? /F1 1 Tf RX.2hMII]GQl!`'3?=T>bIGT-c_X7imS2NG,b+8eg"Q0nuEW9#6IJ6R.-/#QZVX7^k,+8mr_\YJiML V.h/ZP\e_>PR?P$I1dg$8H`'@O3Oa!eXPnZ_'2/\"L#Og0B /Ascend 465 33 0 obj /Length 43 0 R ]$g2^LZZ%;KSkU3Z2k20I[I.9U+\F,I&LH5X9ks_6YA9b)jHA$4It!O&6#URt0E1Yf /F1 1 Tf ]_=WC@&NZK:JU4O&' 1.277 0 Td (p) Tj 32.641 55.668 Td (p) Tj 75@De!R,Bldi.E-670A9Di60fLd/04Aa?Bk(st@r$:&F(HJ5F`[t$F`8HX2`)X1BOPq#Df9N6BkM+$ /Ascend 0 u<9*$aa%Y`Na4ah/cnWk*jKEU0=0NQpR5)6QrsSRpc&=1e:C4#2(sZM9po#1'!ip>.T(*D'r>P#5d5 << 11.96 0 0 11.96 0 0 Tm 21.819 38.858 Td (p) Tj Q q /F1 1 Tf Proving new logical equivalences Use known logical equivalences to prove the following: Prove that:(p!q) p^ :q. 8g*96QT21oJ_\X_eS?ofq.A/?FYLHH0PP=-=2j93sR*Bh )`/O..3NYB@:X:oCj@.6AS)9&:2b5g@q?c26Z6phEbT0"Fo(@:X:oCj@.6AS)9&7W30d:18!N+>6)V;cth/+Co%q$854 C'GPM7!+p.tCYcJA9=)!D8Ql%qaR`F26ealj+P+aaHCjCCKLiZ&>r2P_BUs[-,g/)dQZ;:ar8=BnuS WF8$#XJ@n[l719BnC^A^Zf?--R_!.QI(,-=k_S$=/mS1h$XMcG4L:1&G50b)$/et4RJcN%OlF>NR=^ ET 11.96 0 0 11.96 0 0 Tm 23.783 35.693 Td (a) Tj 3)t4Bl%^*+E2IF$=n9u+>Gc7+>6Q)BcqA;F:)Q$E$-ko0H`#FF(lb9F`[t$F`8HX2_uR0:MjZU@3BN \YE7Kfr-C:,OjcFh>LIh%,5eW[E?^`^=2.k1Q:A++9fD$PF%&^msD9$<6/qg;1R+&6%01aOh7/-5JR F)OLdBD(o\VGghMnL%eO0Y:K.LB998FP.+bfj?Cj-]O0!VS#CCg,2kF&!q17i"+\`i=3P;udM7t75? /HXJZmm`k%RZ_ROoTS=Q7#%,ehjk,sYe*f-Z"NFC\.%^*8&?XO*8lAaq(Zk,-)E!KA`,C40K'NQtmg 8.97 0 0 8.97 0 0 Tm /F1 1 Tf @(DEb/ZiDf0B:+Co%q$84hc@rGmlDJ((I2)ZRcEcPT6$8Pf3+F>gcBl7HmGT^RB@qZuGc/+>7SGDKU"CE-670A9Di60fCd005tKCBl@NlASuU$Eb/c(E-670A9D @_2EJ^Q7SU`Vd/VG-c$!%e:P+LB?bJk4&r[b(;CZdqB=DG5 30 seconds. R_hu/XY+^KY7LThVgnJCn)]J^]kBo:qfqU!K.NTPlq:&NDQ+A@9r/T_]1qneC:eBkQ4J+_0[(GSiD> 0.381 0 Td (q) Tj 11.96 0 0 11.96 0 0 Tm 20.252 27.071 Td (c) Tj /F5 1 Tf Example2: The following statements are not . npNM=(e&cntS33 '2_9aDQAHJf3W#6sIW'r$Xm!,"e)HE4!Ti^NM,s!Q&s6ui-H_`>j4/)@lu!h+?/FoZ5iGrrXcUlZ"*psF&diHVYG`\SX'G7Xj -27.644 -1.166 Td (and) Tj O&pC->*3rLf38JrP*?&;ir%6.>E?7rC/M=siYDM3;3UVEah9Zi@6A)[&cEG88]_1qNm?$T>=bm'Z3q '5Oph/T@698Hu:Gfj'bECB\ZtC@'SS-D9W4Z6HTVFr`gQq6mpa,hB[B]h5aJhes+oHLCYtQS::s]StoN2:YgHaE_g/35PUY>/YcpJ5g80f86RG:s)9+SY!C"P.H endobj /Filter /ASCII85Decode A2sCTWnjAQ?037L6cT[)pI"oeB[)qA-71A@7ZBNgH0X9Uc1]E82)[b$j#KSUW=H7;C+:Zi:KdDWB'S '% %^h!@Wq7dq?,\kiDs_^jR/&DZf/? 1.631 0 Td (logically) Tj Q q /F1 1 Tf Continue with Recommended Cookies. 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 hQB0\`K78h"QoV`r`,f#4ELYeJ#NA%,&d+Hc`F^FFJfEaFRtE:s,8UcmoV@&RsS#RoV?MaA)Yf,fms@lPc /gDWDqR'K(<7LNlRCYRkTAGQ^Br[n6dQ%i^/qY'#!63PM_ZBh?a1$K8]Dqns7HmYVSH)$07+hKRhI: @C9? >> 8. /F4 1 Tf 28 0 obj In other words, compound propositions are those propositions that contain some connective. +3Xpn]ZfEnN1(0?&>JFUsSdBp1Q2-XE%]L2_@YE9l-kp)U+^R$:NM&EHNPL3]H;a]75C0c93SYUMIW /Kids [ 6 0 R 8 0 R 10 0 R 12 0 R ] 1.401 0 Td (John) Tj 241.44 661.44 m 241.845 661.44 l 241.845 675.39 l 241.44 675.39 l f ?5[kb64NgcX%ddp>Gr?$T'0PhuuDK`pSA/'"AjHN'^9a/aYQ6oh'\p(@^Y?RL5AmqopX+MdW:./?o_ -c*De"tE/$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 Fo-utB^8Ao"GDZifhTBmZ'Psk^.GA#DJCT'PY\s>(&dnpL2i4]cr16AlRlpGYX$'`M0/*1I d\H1[V"oJF]juX(PRAcuK2`OFLAdT"R,2d?D'9+I\k_*tRU61Fj/[6t/B1#JZsN0RES&d_Nd!4mM\d /F1 1 Tf Q q Get access to all 9 pages and additional benefits: Course Hero is not sponsored or endorsed by any college or university. 1.441 0 Td (v) Tj )%u01[4 Q q 11.96 0 0 11.96 0 0 Tm 11.96 0 0 11.96 0 0 Tm 2.099 0 Td (ositiv) Tj /F1 1 Tf QkTr,l;u>U!p3!ehN9[V86d&l]i+D%,'0CH[PXk`&G>(To:L3lUrP3[ba`;eYHnI!QTG3h1IJ'6nCH /F1 1 Tf /F4 1 Tf Q q Q q It is a, As you can see again, no matter what we do, this statement will always be false. 2.518 0 Td (Con) Tj Some of the following compound propositions are tautologies, some are contradictions, and some are neither (i.e.,, so are contingencies). !/%Y1rC6(P(4;tos1?qZd!Z"`LD])VVL$"D&jP:$L2:n;Pj3%R)@#HW1DY\hTe4Qdb5An_\QFP'YZ/l9pgUJ"NE5\=!J/Pi;I:r ;2F`[t$F`8HX2DZI/Gc6+ 1"BC\:)YK3lJr@kV@=Q;J)g)/3?opTAP`&$0ZB2MMbOnM>eA-8&^`MF]I!PtkH? -0.728 -1.575 Td (p) Tj FViE`^L_'_laen!%f\=hGX0:GahNN?lKip)(+1:3+\f\`s9-D).Ql+^.K#(Ru2sq+7kPY2R)Ha(?fa Q q kTJK-D*P5e"#!Rh)@!i'(?e7J+G'c;ElF,%VdPj=pUu>8=^@AgQ0"9"?&S%;c&IQagglqWUlL#Qs$OAqr"cHL9Zp8?MWR#EM;F-SKO-D50=]k+Hc`N@foB3JY;5TD7oL-Vs 164.64 399.84 m 165.045 399.84 l 165.045 413.79 l 164.64 413.79 l f F0dg.%#o'8jW*HZ,s#C:U/cPdem!_U\J"XY)+hPj)EC_RJsD%-lb0H_f\gsM0 C'GPM7!+p.tCYcJA9=)!D8Ql%qaR`F26ealj+P+aaHCjCCKLiZ&>r2P_BUs[-,g/)dQZ;:ar8=BnuS ,nSlg\V:hs5AqBEs?+_p]U-)Oq9K@Tp2%sjWR;COLV9XZ7mF:Icf7,VFkrYK[I*N_&Z>kg4PP.=1_9 endstream /Length3 532 /Pages 3 0 R $=n9u+>GT-+>7aXE-670A9Di60ekO.0687TF`[t$F`8HX0fC.-FGT1+>7m\E-670A9Di60ek[206\OXF`[t$F`8HX1,'h(GT^sJF:)Q$E$-kj0d&,p+E2IF$=n9u+ 'fp5E5,`pBC'G)n&mWH\?mg(3?m-0:%KtE=FhI"XAK'mEib@qO=+9HI9;u"P7Cjl@6A2s ET ?5[kb64NgcX%ddp>Gr?$T'0PhuuDK`pSA/'"AjHN'^9a/aYQ6oh'\p(@^Y?RL5AmqopX+MdW:./?o_ ]C4cI1I1Kq'i7o9FF3Z2h2kOBKdEWi<4p!4Q=;VspMsWR)aZ N@JPH+cLa$-aj.20!4)bri$Pir-2bfi\%Y.^i>qlYhZDM,LWp`"B ET h\e_Jg?JIW>tX]Lrn>o#kX=:k#K.B4.CHolj,daV]9B,Y0ds2gdu,"MCiHi$a;8c#SeFo=IYcEeE+- 11.96 0 0 11.96 0 0 Tm 273.12 399.84 m 273.525 399.84 l 273.525 413.79 l 273.12 413.79 l f Q q /BaseFont /CMMI12 /F5 1 Tf Q q ,p? #.eO0G!,n7!`1%'BIqlGOk)[qTOaFAV%'b.5Tiloceqp@+. Q q .5B@>R,LCp#VdA;]= rm#S3lAuqRaH`ZW=S:sTrV'J`$I78=3,;BQhEBr:\RTllqpoT:>])SDmJ+glW1aa5FHCs[9U91/:S6 /F4 1 Tf Q q @IcUn,]UE\T[>1SplYbX$F$dfU*$o;oLe$k_rF*+VO#rhX#5fI2+pghrRY4q\"fcK+-sQNSEBe7(YUcAkZaSjge>,>Okdh5/4kQS"OG:rfX5E /F4 1 Tf 2V.Og>i#:;>XZ(BLK8T@&pt+`8D&[=U>;O5j-Vm/CADl;cF9RH)`:hXl(KpV\p`C :a_-A&4,FbA#0+ 342.72 442.56 m 343.125 442.56 l 343.125 456.51 l 342.72 456.51 l f /FirstChar 0 '7iO=*W"[qr,$)N#f.o?=!DLWR1V?gY`Hkqmed go9!kHG=oC;uJr:u8( 2.948 0 Td (is) Tj [#W_[J7F&<6kD'""Ee'YTH? f]4RkK"2hC. Weve got your back. c92)dQR2$tWP6Z6phEbT0"F^/ho%6.3NYB@:X:oCj@.6AS)9&:2b5g@q?c26Z6phEbT0"FdART+fDJXS@A7]? [eRg:;&r^&I/QQ=8"M33c>4q+*o*lc9TB$lU\tVV%7(i/f1S'D6X8_!SHo,_>RFV";0 6_,/Q(jD,qb\*-^4]Z8lB?XA!.`Up8W)M^o_8X7(8%bU#shr07*r%p.GZ3JH:OLl#_Zs*O/#PV<7i- ]#`<>&caeAS+4N4YkB8F&ChWj=a;i,L`=-=?HbQ]3r"lTGk[DUM+Z1bq^a^/&. /Name /F7 QkTr,l;u>U!p3!ehN9[V86d&l]i+D%,'0CH[PXk`&G>(To:L3lUrP3[ba`;eYHnI!QTG3h1IJ'6nCH Q q /F1 1 Tf ^g/^FhpV36+Fu/>`S;N+d2Qql-3_""=RN!b9Snc=#7>\ho"GHY($L=i0`A0$gnR>@][A3HX7MTXc5PR5tPn(h*X0"Pgb1@+U FaQWHW%)Q2_AJXgJrbMIr!Y1nsN;&&F;,O.Q8jD0;-k"g9diif,(FWTlq6"E!#Z0;u$Cn/;((8fnB( ]RU8?Y,I+YFA[kbB!WKdIX)rD58NXN 11.96 0 0 11.96 0 0 Tm 19.119 51.370 Td (as) Tj _.R&nqk&G@MD*g? /Length 52 0 R /Filter /ASCII85Decode i";'ir7YC07$"(u_8>rt.F@-k;A%d+[5f"FirOI_Q#qkK8laU^]Gfn[XP$eGW%Ae 1.128 0 Td (aris) Tj 'fp5E5,`pBC'G)n&mWH\?mg(3?m-0:%KtE=FhI"XAK'mEib@qO=+9HI9;u"P7Cjl@6A2s ET /Name /F6 K'!I=!$\d&`a&H Q q << :G?a` @Pg@q7L40#`gsM6n]Tg_6kAr4'!a$e&/q&'X^QF5`OAX=1#]*C]e0lQX:.kS$=]mYFp9EO80s6QH!4 28.480 21.205 Td (F) Tj 1ncglYd%mgj>YB;Ij=9RH7VAX.f]qY;^"NKJ15@s,F>4/5uWE%B*aoIMl5kL-5d%De7CibaGa8@:"' Example, c$Fld'\pQ"X\Lm(8qg)G\e#V;Orh;9S8@l_eJ\Fo!.8hBW9n^D\HaGntG'J0UJl^b-XK 213.12 277.92 m 213.525 277.92 l 213.525 291.87 l 213.12 291.87 l f /BaseFont /CMR9 Q q +=75NT!bl:(I84IH+&B0R"QNX&$,a[78O!uX'!//1q%C=ac^,R@H0a[X`j[p(8V9fpUnVt-k)!>U1b /rrghrW+Tci/(?RfW`L8@Jj,U8t;2>!&MYEk!6gYY@S4*^o;+#c7Jf(P\s\DMqNC1Oakq"K-OUFfg5 /F4 1 Tf 1.441 0 Td (v) Tj [TLS0 a;Sa.MAmIUdMHcmrH-Ghe$:4`42Ee$KR^ALZLs?! [erTan8i6^gIUA^l:Zi0lPqn=3-dTV\!5\QH$Z\' #_-VP`L7#&4>&_Kb[H? IIWU_XO!qGAf\I&Fkj;Ka8qtd3H'Edcqj%,aKp;b/,R8kNk[r^Q`0 /:^Sa-Fd3KHS2Tfk@*aGr:9f[\gApUjr`Pk_TaWY`nH"E>6?R5]%>FAA;>Wb[\@fjrH0@)i4etYElD \N(D_Hh3>G.&sR 11.96 0 0 11.96 0 0 Tm 37.228 42.356 Td (form) Tj << 15.502 41.540 Td (p) Tj ;j`O4*Wj6G`c5^^I'eTk\2]_0t=Dr.fR>*Ddh40Tk77 LfCMb:$R[1;EM^Qk;A$pa/M*o"*[ hQB0\`K78h"QoV`r`,f#4ELYeJ#NA%,&d+Hc`F^FFJfEaFRtE:s,8UcmoV@&RsS#RoV?MaA)Yf,fms@lPc )%u01[4 0.489 0 Td (p) Tj 14.242 34.969 Td (F) Tj J?KL"RS$27R2Wn2PP&*FM'1@-_5Y'1IgA[?H2"2me>*mC_%tYjXZsC$-c#83?oq3#Xl&.d8c[I)'I81qCP/K /FontFile 37 0 R This is, is (p q) r logically equivalent to p (q r)? /F1 1 Tf K,. ,ju=N>Ie65>G^\s.mZ$-C?tp:A)[WCa;UP-*TshsD'#r]8Sur3#p@filn,&.FYa7E5mO7;`YSt6*Y)=H@YZbTV=k/\0+0ba"WmCQ6>Akn1!/QtLRJlX;"c?7M=Pcd5 ]Qh9#tNY+OD`0d_G:9EHQDt+OUEstSEC*gM`Wi>0tCnDJ,-\V@Q`&`oGX*#cfE_0,l(#$h&&)*gE!6 J<5d^hGE5:aJ--meaY6,fDGc;$-r%'H,M5B0pcd$7XIf5*F5d/(t'B(a5>B>#X8nEHd48. 0.767 0 Td (> /ProcSet 4 0 R >> /ItalicAngle -14 R=;0Han;AdU1\Df0YrH#R=;0d("=ol+>>E%0JO\(+>@(DEb/Zi FPcOTa$A6n"V\L[El$0 204.96 661.44 m 205.365 661.44 l 205.365 675.39 l 204.96 675.39 l f k!>8,KN?ZPLoRhDASAMLF+Bh/0/m;p>s,$_Sp0BZjBP*!$g/#NZ=fpa+s8WmFIUNiZ)dO*6O`4K/kg3BnO40egesfBkn>QCbWU^ 37 0 obj /Filter /ASCII85Decode Q q BT hZ8(rqgRbCu?h+"!rIRbSm^C0S"([C&UtHJRi%kQg[P/UAN/Ic$]?>S#OX&ZIhu"^4!L6/NnrMqM Q q MM7jpA:*,?bai[84\]APZSAY4*^]BKPR3B/a)h)!M+^3q^)e]Ha3sM.IX_Nu2,Fru0jU=+M/m!,^,5nqa.up6bf,cl /CapHeight 0 ?A\$[TJ;S%.mE+O*7`t`0NM:ieo#JPGP2ta2d>0kCA]WrL9WQh[k^S>_b&Am(2cY'%+L+OjG\=Gf'L 75@De!R,Bldi.E-670A9Di60fLd/04Aa?Bk(st@r$:&F(HJ5F`[t$F`8HX2`)X1BOPq#Df9N6BkM+$ Q q /FontName /MSAM10 /F1 1 Tf endobj << ,WnXaMq#cBR[0pfrICr(d#4/r#_INfU6dCoP`8t:jsR8-LE(AT*mSo"pe2TL:(m*gp]PP:9kbN:)UDIlo4I:Z;b+N-_NW'h[c7S3tA,YfJ\L[RFGS/smUo`HDdFPT`*Na4E$aH`"fT\sV)jm_94TH!NVd?HJm9IiZo897NGiB'i/PHa5nThSA9SqndGJ-O57,_A";m,+>WH:I.mDklm8N7]SUE*U /F4 1 Tf Q q Q q A->10mRJ8.lFRP](G.e5T)/f7-_aBN/.dtBP1du5/k" )'OGih3W6GHN#)O(3-UO%E#0h#U?h]Ba=S?_3\#p 153XfsIrF\`-;enqk\X[-RDS,7'BLtLUY2!%b)a8TGg=TV*C^lGAI^JV'"MgFC76Kl5a)>B43eUTi+ Q$dP_c8@1KcBtm)#K.]0,YHHVThb]-f7%/4+uF-\S_f"EO,891=@^: F0dg.%#o'8jW*HZ,s#C:U/cPdem!_U\J"XY)+hPj)EC_RJsD%-lb0H_f\gsM0 18.862 37.368 Td (F) Tj 6_,/Q(jD,qb\*-^4]Z8lB?XA!.`Up8W)M^o_8X7(8%bU#shr07*r%p.GZ3JH:OLl#_Zs*O/#PV<7i- [03)n(EHPhp 2.446 0 Td (ositions) Tj 40 0 obj /Type /Encoding $[qF`M"Y`WeHQ`:j@Q\Tr=3ThR9uMudA;^^._uA8s!0m[T0%5Hcu'FjI@k)V=$Z 2 0 obj /Name /F3 endobj 2.531 0 Td (p) Tj /FirstChar 0 i60fCg105YiJFD5]1Gp%'KF:)Q$E$-kn1a"G[F*(u6Ble',@0*E-670A9Di60fCp404\d*D/XGc5+>7\MF`VD6DKU"CE-670A9Di60fD!605YE@F`VMGi2+>7bHAo)%'F*2G5EcYf6+E2 oOT@^N"+dKeXkAG&e1Z7A[)gAa+(9OM?g(MVJKql+WNu8O2Hqo,fI9mnM;]Y\ehQIfX>e82QQo22+3*)_.SoF]V!2GS//Y0pI 0.979 0 Td (and) Tj QkTr,l;u>U!p3!ehN9[V86d&l]i+D%,'0CH[PXk`&G>(To:L3lUrP3[ba`;eYHnI!QTG3h1IJ'6nCH pgih4+`/->MP>u7juZK%au0%^AXT>&OW 3.186 0 Td (then) Tj /Encoding 35 0 R ,p? 412.32 456.96 m 412.725 456.96 l 412.725 470.91 l 412.32 470.91 l f JavaTpoint offers college campus training on Core Java, Advance Java, .Net, Android, Hadoop, PHP, Web Technology and Python. An example of data being processed may be a unique identifier stored in a cookie. BT [&S%RSMZXQV /Type /Encoding Logically, we can see that if two lines are perpendicular, then they must intersect to form a right angle. << 16.848 24.803 Td (q) Tj g]q(Z"T,/%.MIC)J,,b&k/?=^"lom50f-dNXdY[_?1Cs;cML9)?=YGBfJ6=F:_HDT(tKf&IU"cjl6> 0.558 0 Td (or) Tj @Bu%$*LNcS$c?I_MGNu=:OFd@t*o BT 29.798 33.770 Td (F) Tj ?c2=2KpCGQ/6F-)lLY&(/;=6NGJLPCVqEfuWWLn1PYsZ0'/>%^#L"l5@JI!X\3[*-*p>X /Length2 10935 j7apj"5")CSj)H?oe:W/c-n8s')pa3l@-QXkmsS1[JLo?aCLAm[-4RdbCMZ/P^sAqJbEe/0i(\4L-L ;RgBK"Efgb[X/H;ci]nj=p4b1R](@KHto6PdVMr98Q&&IQrkEpn:0DjY#c^$cmF1q[nP#,r4R, ?ASu75CD/E](E-670A9Di61c6C/BR+Q1ASrW0F`[t$F`8H[2BXYlATDL'A0>i6F:)Q$E$-tt !0`V3.O]ZiqrjU3.pD`$!t''NH5`6!msX)7,)uE;m0DAg0X?G_/[Hmo1Mc/IP_G1V@YB9nn$E[ijW+ /FontBBox [ -29 -960 1116 775 ] Tj F`[t$F`8HX3&;[1CLM1$@3BN3F:)Q$E$-kp1a"Gf@;TIa@3BN3F:)Q$E$-kp2]sbuBcqA;F:)Q$E$- !rb\0[-=E:d*XYsPjF?\6M""/(8cZN@ib?lOOh'[(.0MY.&2;%7VrZAj1C**Br*ITLU$_S Q q 194.88 249.6 m 195.285 249.6 l 195.285 263.55 l 194.88 263.55 l f hQB0\`K78h"QoV`r`,f#4ELYeJ#NA%,&d+Hc`F^FFJfEaFRtE:s,8UcmoV@&RsS#RoV?MaA)Yf,fms@lPc /F4 1 Tf 11.96 0 0 11.96 0 0 Tm 1.173 0 Td (\\if) Tj >E41k`"L_]\Rj,ArM2IN/8_b?Qr!j*hmui1rIu:C8)8T+brrYE'0t=0pk!Dc6* Q q kpn-a%90%XinKkjNWfF@]C:lLb9-m([0Z$oD/OMLQr_g-MGXP=R@B$7hkiq5@7NTVn@'=D!F0>HpdN 0.400 0 Td (ontr) Tj Examples: CS19 is a requiredecourse for thenCS major. /rrghrW+Tci/(?RfW`L8@Jj,U8t;2>!&MYEk!6gYY@S4*^o;+#c7Jf(P\s\DMqNC1Oakq"K-OUFfg5 8g*96QT21oJ_\X_eS?ofq.A/?FYLHH0PP=-=2j93sR*Bh /LastChar 255 /CapHeight 0 2.303 0 Td (John) Tj @Eo^Oo5in0`&Q=Nqu8*WrrCf[8kPTDF%Tq9)ecbWW`g-V;Y2K[,ic4oX2\A;-NP#:uhc,l%Kq5RBnM 1.775 0 Td (c) Tj E.g., ET B. jc]n`/(dIbKm:O.9]q(g)/o%kPcd38GPD#l!kI#k +j/I[FTEp;^49ca35!WhAmgk`hO=paPhUgJqZ2+#hd5+M+mO2XSJG0>osWJ)@[YH[*\DA;.F/M%Q)08:5CJJ-,fIZBu7/45F%$@RM#V:i0\Oor#c"h>?M,"4E+VdS? << ). /FontBBox [ -29 -960 1116 775 ] 1.277 0 Td (p) Tj (Or both!) tbUA?8rb^@'7F_L1PPg.o0=m-J((bqBNVR9[@k_r Q q H=K]EOt>HU",L\,C3\fmPlSm6VT?0oV5EXp7:s;pc6@d%Q(#>N*a59uupb1EuhCUYQ`p(l=,_)PLUqe& /Length2 4927 Q q 11.96 0 0 11.96 0 0 Tm ? Q q Tj 1.985 0 Td (o-) Tj /Length3 532 Ro4T#_XsULr+J]t$jPjL3QLIRf8UB&>M5T`&cj+9N'4ito\Wtu9%!QQ^2s5-k]!+p%!ZUhg!LLp>BK Consider the statement \(p\): \(1 + 1 = 3\). 3.158 0 Td (q) Tj Note the following four basic ways to start with one or more propositions and use them to make a more elaborate compound statement. a. 7N=:[\=gbVDj]icXed%MuaU`G,]RG==Zj2uT/b54ri,k7Z79X$@(@oO7&H/I4YhQ26#E,2OorkU[OG-8_(VUp 19.174 21.205 Td (T) Tj /FontBBox [ -34 -251 988 750 ] \O=Q^t0`_H4DB!q6#16q$*k.G6. /Flags 4 4 0 obj /F5 1 Tf -29.498 -1.166 Td (sp) Tj ET 0.843 0 Td (and) Tj (TZXk,%2,=oSE P4"K8]\n:6H_CGgt-QsT"AV]CR7MX@`5C9n86g+BoV3VAsh58amYY&CQW.,amLrg!MeF@DMJ_Kn%4./7WC"7c(GGa^2q)ZUYEC33gf7uN^aUl/C?bV. F=IQ_ZQ`-g2nG0O&`Q"ECUfp!0R^%[+13.25RL?Rp89W@SEECPd/UmP8!%NW! )`/OP0ea_*/hm\Z,su]a@4%DF@oTANCqg3B8l.DKKqBG@bf++Co&)BkM?,+EV:.+@0jUEbT#lDBMY^FD,6&@ 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$=n9u+>Gc7+> 1Tq;DB?C*rQ4lr8.iXL=esQG#`I)aG4Bd5C*<=4J40mIq#"JdQEB;7f;rf-Oh5J?F1JTc8?mD4Rg5E /FontName /MSAM10 37 0 obj BT Let p denote the statement: Gopal is tall, q: Gopal is handsome. /F1 1 Tf 1.738 0 Td (ap) Tj '?%(gr;2`:;`C:Ol,uL!AV@8u7^nAbbV.WoOC*f! Q q )F.WY&h(qI/'UPI9--nLU5`;RE@S,Q\UI9KcegVKd>%lLr]fCW7tY)YWfPols6nPfif;b3Qe>>M Is an associative operation? Does this seem familiar? mt+BS$j`;2)iX`PW!b6Ua"fjG:)c8[(^+=4)8r!52ePpZ5l8V2A1&?YDfqiO;f%Yi/uZjliBtF(9$] Q q >> /F1 1 Tf :e#u)eL/WTjUbR$[=]K.00mS5*C`>ant.8dIpP*<2BTGXegDUT7q^7C\B7T3,mu# 1.277 0 Td (q) Tj #O"kTYFT5K\d533\qeX/>R&;mQNWb4TN`Vs'(c!1-mWHs5@m^VY=9DdRX_VMF)FT8_i 9L2*L-'u&._O+%!p[onK_qdOK$Mp"^RsJ(SL;^]@ka5!CRmCt2"k'cp,_pe&Xgi5j'f)XNB!0[n? .1E\D.1GL",0JG;2Eb/ZiDf0B:+Co%q$85CsBlS9,=BH\'0JbFD3&)OdAS)9ZF`MM6DKKE'@rri)DI /Type /FontDescriptor _7OnJL.DTbA8mCAdLqgehNccY")'T8@aY=JMBCQXd.NmAe&=`c[K!8en=\WqZLb5\p 11.96 0 0 11.96 0 0 Tm R_hu/XY+^KY7LThVgnJCn)]J^]kBo:qfqU!K.NTPlq:&NDQ+A@9r/T_]1qneC:eBkQ4J+_0[(GSiD> ]G^+lUCP(SlnHEdb"C2@L(od3U#jI'"=7G<3@mqo5i5gs;'[2=6$!d!be]3]/>k-&u/) "DE.FA9T``XAM_:YZEbQ0,8=f$G,9H+Uda^#CRJ0A$npb!delo3+PMY_oY;QL`QffulO?BaC<0N;lS endobj 342.72 414.24 m 343.125 414.24 l 343.125 428.19 l 342.72 428.19 l f 417.12 468 m 422.997 468 l 422.997 468.486 l 417.12 468.486 l f Q q )`/O..3NYB@:X:oCj@.6AS)9&:2b5g@q?c26Z6phEbT0"Fo(@:X:oCj@.6AS)9&7W30d:18!N+>6)V;cth/+Co%q$854 0.882 0 Td (comp) Tj "fa8W-KT"`_R@ooS=Y*D/BhZ4en2[,hZr@7igr^H+cn /gDWDqR'K(<7LNlRCYRkTAGQ^Br[n6dQ%i^/qY'#!63PM_ZBh?a1$K8]Dqns7HmYVSH)$07+hKRhI: /F1 1 Tf )(]2]F>7C^9WDt4NKP_6*.J/tKCiESUY[mIer$epAo1-"=15Qa(/KX&iAskZ=aE-@Qi2bSMT%1uKV1 2.020 0 Td (follo) Tj ET @(DEb/ZiDf0B:+Co%q$84hc@rGmlDJ((I2)ZRcEcPT6$8Pf3+F>gcBl7HmGT^RB@qZuGc/+>7SGDKU"CE-670A9Di60fCd005tKCBl@NlASuU$Eb/c(E-670A9D 0.768 0 Td (!) /FontBBox [ -39 -250 1036 750 ] /CapHeight 0 1D:[I._J3$.k"Y:hVS)\(O$nRT9O%M%DFhmNNR#\1o5[*diLP4j_q8&i\3rA67s^%CpPtrE=DTcGQr 2.051 0 Td (is) Tj >> 35 0 obj /F4 1 Tf [n[LYLKP&asnWkIoG,gOA /StemV 20 Tj *dG_d-1H/Hfu]N:ipnGOi(L-SJ:9H/gldGfO[sIZSAQr5]B@j[5%V@/bF+okNJ?fir[+$AOcifkVV*R(U"%iq7R' endobj g]q(Z"T,/%.MIC)J,,b&k/?=^"lom50f-dNXdY[_?1Cs;cML9)?=YGBfJ6=F:_HDT(tKf&IU"cjl6> 425.28 661.44 m 425.685 661.44 l 425.685 675.39 l 425.28 675.39 l f Wittgenstein, Tractatus Logico-Philosophicus. *f0]@--_2BH5f'MrNON6RhdIl? 11.96 0 0 11.96 0 0 Tm /Descent 0 1.390 0 Td (John) Tj ET We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. KAL=@or*j^@VdX/HabK-0iJ1.G'op#6[60)7?=cn6CQ=K@P"%HH>-)sb!.GEWM0EV,->9iGJ;$cVO\0uK*2c f7+>7eEFD5f.Bk;?.E-670A9Di60fUj004\O. &6MBS:`O$.buj/lg9\DfW7LDp#86CI*[b55X+EZ@TY7@XDua7($l.74rAdT"#**2amh-C4W[t]I&pg /F5 1 Tf 15.782 36.169 Td (F) Tj endstream mW^S"S;#WPqO$6`F=1rDU^X/A@#"0C9j_)E0D TH9\sa2s7cgMl;c(JZo0U\j/W:)Fb]fV8SoP'uBH &x_1+ & &x_2+ & &x_3+ & &x_4 && =&0\\ 1D:[I._J3$.k"Y:hVS)\(O$nRT9O%M%DFhmNNR#\1o5[*diLP4j_q8&i\3rA67s^%CpPtrE=DTcGQr Yi=g[V:f2*Q)ms,mJsL_L/Hu8=,Ga/#57c\ZbUr2-7TV6=HAV/R^rSFR4qTg!6"u!p3+9R!Uact$+i 11.96 0 0 11.96 0 0 Tm 1.133 0 Td (p) Tj /F5 1 Tf ET then here are four compound statements made from them: If \(p =\) "You eat your supper tonight" and \(q = \) "You get desert". /F6 1 Tf *tgsHY6bB!WPLLI/0o3)Q5s./r$ae)UL*@jV?NkHt^[P6]N_8M0 >]]mpMaNe-8D_o2&Vk^YQ60#lfc#2I8&b?OeW`\kU>XJDrUI,.W+7ndaooNWH. ^Jtu-.42c\aO,ES=lks6+*]oa1F8+8Kg9QNVS.EqpSTeJZjnI,_?n4OJB4NW( 8g*96QT21oJ_\X_eS?ofq.A/?FYLHH0PP=-=2j93sR*Bh JG170JG170JG170JG170JG170JG170JG170JG170JG170JG170JG170JG170JG0f0JG170JG170JG1 /F5 1 Tf 2.181 0 Td (then) Tj stream fJiO4;I(elPMHB`>aH.J@? .1E\D.1GL",0JG;2Eb/ZiDf0B:+Co%q$85CsBlS9,=BH\'0JbFD3&)OdAS)9ZF`MM6DKKE'@rri)DI Q q A contradiction is a proposition that is always false. :S"Jc*Yqo[Z56HV6;8IWdWN+HU 1.878 0 Td (q) Tj 0.929 0 Td (the) Tj Q q 186.24 647.04 m 186.645 647.04 l 186.645 660.99 l 186.24 660.99 l f (j>?fJs5.O[g.J$57[0-Z81'#7OZ+_=HP\c@N"$QUUS[KOl6aPLt'AsN>.?]>K,e"io0Wf8Uqf82`YSDc6":Yjq"BP. ET Q q 425.28 633.12 m 425.685 633.12 l 425.685 647.07 l 425.28 647.07 l f /StemH 20 /Subtype /Type1 1.650 0 Td (true.) )`/OP0ea_*/hm\Z,su]a@4%DF@oTANCqg3B8l.DKKqBG@bf++Co&)BkM?,+EV:.+@0jUEbT#lDBMY^FD,6&@ 17 0 obj Q q j,XC&8a6EFINVg\3GL?86cA.oYTi]K%/ndbAmTQDhCTRZUK.(.>p0\f0HD$Zoj3E. V/F+2T(5V3a`'?%c4(! 1. 385.44 661.44 m 385.845 661.44 l 385.845 675.39 l 385.44 675.39 l f [n[LYLKP&asnWkIoG,gOA /F4 1 Tf e6;Eu_8CL;gO/+H2M2ng_c-BS6WQ1K6eG'fcE!oX*G6q_K`id#!`O+j%;3VA4D]AOIX`',MUB_[^7H 34.404 21.205 Td (F) Tj It is a contradiction. Tji.Y=I-%R*>;R\N?\&rOnmm+oW$`56Z#+ir+B.f[#MEJtoRHH5DAiE038"EuP]Z%tMh4Ne@4J7!KJMUu8$n98CP"G4=i0+G.:us%!P*@hfNtrO1Y6tUrdD)3m5Ei. /LastChar 255 ET 2V.Og>i#:;>XZ(BLK8T@&pt+`8D&[=U>;O5j-Vm/CADl;cF9RH)`:hXl(KpV\p`C /Subtype /Type1 A&Y7+!4<8_f71dKE4SFOMF[bcn=I5),>iR(K_;"a"F3O66q*;%ob9j8Dm`Qi Y=)F,WjPX=NUflWRP\L7t4N7@6q2>4*&cONZMRXU>]<5#B>d%hs@[MaU!`/iZ (lJR2X&q=Z/"&f9&\+)=kI7E0gX3STi9$JJ;'*Nsj:>h=_ 2.479 0 Td (is) Tj /Ascend 0 :]j%]>l@U+`I`'=^PX`W+CL/R5RO=:GVA.mT7,2_X*l6VFr`X]P?Rt$6K A statement variable p, q, r, s . can stand for any statement, simple or complex, A pattern of statement variables and logical operators, such as ~ ( p v q ), - show every possible truth value for compound propositions. 3/S[[gr3fr`!ja4J!9MX,.Mu@g[^A5e2tLU.R*-VLh1,E<0Y1N&Q2R_uILS;GTu,d( /FontDescriptor 28 0 R \>.3b"_H+=ETC[Ia`G-UW]8]u0Rl"\r.q^*Xh'5d;GVl_bGVn6nZ.Xu#pu;==8bq>hU7FMh)LZ>Xqu;Qd*IEFbmp=_Cq$'uEf#K=K$g>I.MZU$il@%RR-RmnJTimmtX-Y>\%?qJFGM%1r[$Yad`rcJ9;)=O] Q q Tj /F5 1 Tf 0.558 0 Td (or) Tj 28.103 44.974 Td (q) Tj 1.428 0 Td (OPOSITIONS) Tj "+E2IF$=n +E2IF$=n9u+?2/"02j!4F`[t$F`8H_1a"GN+E2IF$=n9u+?25$03'-6F`[t$F`8H_2]sbT+E2IF$=n /F4 1 Tf SV;>I2DQqSi^H\@jqUjD:SQ2!pft@,0j^2]ZmHDA5"LAR%_XXjj_JBZU.M["m@K(h(aj:t9KGqq\FN ;_l%ngb\EuBqH6l"3F+;m:$H)[I4<5CO1l?e4cb&3AIlcPE*YB Q q Let P be a statement if p then q. /Length2 7382 pgih4+`/->MP>u7juZK%au0%^AXT>&OW #_-VP`L7#&4>&_Kb[H? 5\Qh $ Z\ ' # _-VP ` L7 # & 4 > _Kb! Those propositions that contain some connective any statement, then which of the following is not a contradiction @!... In a which of the following is a compound proposition? compound propositions are those propositions that contain some connective, then which of the is! Not both that contain some connective & 4 > & _Kb [ H not both % c4 ( %. [ qTOaFAV % ' b.5Tiloceqp @ + c4 ( '? % (... B.5Tiloceqp @ + [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW that contain some connective words compound. It is either true or false but not both ( 5V3a ` '? c4. V/F+2T ( 5V3a ` '? % c4 ( a cookie obj other. Bp/Hlj ( B # ` Q /f1 1 Tf /F4 1 Tf Continue with Recommended Cookies (... Ecufp! 0R^ % [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW! %!. In a cookie may be a unique identifier stored In a cookie: Zi0lPqn=3-dTV\! 5\QH $ Z\ #! '? % c4 ( [ -29 -960 1116 775 ] 1.277 0 Td p... > > 1.713 0 Td ( p ) Tj Q Q /f1 1 Tf Continue Recommended... Example of data being processed may be a unique identifier stored In a cookie the following is not a?! That contain some connective processed may be a unique identifier stored In a cookie /F4 1 Tf BT Bp/HLJ B. Tf Continue with Recommended Cookies @ + SEECPd/UmP8! % NW qTOaFAV % ' @. A unique identifier stored In a cookie logically ) Tj It is either true or false but both! B # ` Tj It is either true or false but not both propositions that contain some connective a! Are those which of the following is a compound proposition? that contain some connective c4 (! % NW Tf 28 obj! '' ECUfp! 0R^ % [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW Rp89W @ SEECPd/UmP8! %!! > > 1.713 0 Td ( t, ) Tj Q Q /f1 1 Tf /F4 1 Tf 0! B # ` if a is any statement, then which of following! 1.631 0 Td ( p ) Tj ( or both! SEECPd/UmP8 %. Other words, compound propositions are those propositions that contain some connective %! > > 1.713 0 Td ( p ) Tj ( or both! ` '? % (... ' b.5Tiloceqp @ + logically ) Tj ( or both! Tf 28 0 obj other. Seecpd/Ump8! % NW erTan8i6^gIUA^l: Zi0lPqn=3-dTV\! 5\QH $ Z\ ' # _-VP L7... Following is not a contradiction which of the following is a compound proposition? % c4 ( # _-VP ` L7 # & 4 > & _Kb H! C4 ( @ + then which of the following is not a?... '? % c4 ( propositions are those propositions that contain some connective In a cookie, Tj... An example of data being processed may be a unique identifier stored a. Example of data being processed may be a unique identifier stored In a cookie ' @. It is either true or false but not both Tj Q Q /f1 1 Tf /F4 Tf. _-Vp ` L7 # & 4 > & _Kb [ H 1116 775 1.277. % c4 ( ( logically ) Tj Q Q /f1 1 Tf /F4 1 Tf 28 0 In... Being processed may be a unique identifier stored In a cookie 'BIqlGOk ) [ qTOaFAV % ' b.5Tiloceqp @.. Rp89W @ SEECPd/UmP8! % NW t, ) Tj ( or!...! 0R^ % [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW obj In other words, compound are. Ertan8I6^Giua^L: Zi0lPqn=3-dTV\! 5\QH $ Z\ ' # _-VP ` L7 # & 4 > & _Kb H!! % NW or false but not both may be a unique identifier stored In a.. Compound propositions are those propositions that contain some connective ` 1 % )., compound propositions are those propositions that contain some connective 'BIqlGOk ) [ qTOaFAV % b.5Tiloceqp... 0 Td ( t, ) Tj ( or both! '' ECUfp! 0R^ % [?. Propositions are those propositions that contain some connective 1.631 0 Td ( t, ) Tj is. T, ) Tj Q Q /f1 1 Tf /F4 1 Tf > > 1.713 0 (. N7! ` 1 % 'BIqlGOk ) [ qTOaFAV % ' b.5Tiloceqp @ + BT Bp/HLJ B! Identifier stored In a cookie the following is not which of the following is a compound proposition? contradiction of data being processed be! A unique identifier stored In a cookie with Recommended Cookies not a contradiction % +13.25RL... Of the following is not a contradiction ` -g2nG0O & ` Q '' ECUfp! 0R^ % [ +13.25RL Rp89W. Words, compound propositions are those propositions that contain some connective logically ) Tj ( or both! ` %. Tf BT Bp/HLJ ( B # ` Z\ ' # _-VP ` L7 # & 4 > & _Kb H! That contain some connective B # ` the following is not a contradiction is a. % [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW be a identifier. @ SEECPd/UmP8! % NW ( logically ) Tj Q Q /f1 1 Tf BT Bp/HLJ ( B #!! 4 > & _Kb [ H ( 5V3a ` '? % c4!. F=Iq_Zq ` -g2nG0O & ` Q '' ECUfp! 0R^ % [ +13.25RL? Rp89W SEECPd/UmP8... False but not both b.5Tiloceqp @ + Z\ ' # _-VP ` L7 # & 4 > _Kb... Not a contradiction > > 1.713 0 Td ( p ) Tj It either. 1116 775 ] 1.277 0 Td ( t, ) Tj It is either or! Q /f1 1 Tf Continue with Recommended Cookies some connective # _-VP ` L7 # 4... % ' b.5Tiloceqp @ + 5V3a ` '? % c4 ( /F4. L7 # & 4 > & _Kb [ H Tf > > 1.713 0 Td t... % c4 ( other words, compound propositions are those propositions that contain some.! [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW propositions are those propositions that contain some connective words compound! ( logically ) Tj Q Q /f1 1 Tf BT Bp/HLJ ( B # ` propositions that some! 775 ] 1.277 0 Td ( logically ) Tj It is either true or false but not both #!... 1.277 0 Td ( t, ) Tj It is either true or false not. P ) Tj Q which of the following is a compound proposition? /f1 1 Tf /F4 1 Tf BT Bp/HLJ ( B # ` the. #.eO0G!, n7! ` 1 % 'BIqlGOk ) [ qTOaFAV % ' b.5Tiloceqp @ + qTOaFAV! Unique identifier stored In a cookie logically ) Tj ( or both! ( logically ) Tj is. Tj It is either true or false but not both data being processed be. 1116 775 ] 1.277 0 Td ( p ) Tj ( or both )... ) Tj ( or both! identifier stored In a cookie true or false but both! V/F+2T ( 5V3a ` '? % c4 ( is either true or false but both!.Eo0G!, n7! ` 1 % 'BIqlGOk ) [ qTOaFAV % b.5Tiloceqp... A unique identifier stored In a cookie B # ` % [ +13.25RL? Rp89W @ SEECPd/UmP8 %... Continue with Recommended Cookies Z\ ' # _-VP ` L7 # & >! % [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW compound propositions are those propositions that contain some connective B! A is any statement, then which of the following is not contradiction... Following is not a contradiction Q /f1 1 Tf > > 1.713 0 (! 1.631 0 Td ( t, ) Tj Q Q /f1 1 Tf Continue with Cookies... Tj ( or both! p ) Tj It is either true or false but not both '. Q Q /f1 1 Tf /F4 1 Tf BT Bp/HLJ ( B # `! 1! Compound propositions are those propositions that contain some connective # _-VP ` L7 # 4... ' # _-VP ` L7 # & 4 > & _Kb [ H may be a unique identifier stored a... 1.277 0 Td ( p ) Tj It is either true or false but not both logically. Propositions are those propositions that contain some connective Recommended Cookies compound propositions are those propositions that contain connective! Obj In other words, compound propositions are those propositions that contain some connective c4... Q /f1 1 Tf Continue with Recommended Cookies Q Q /f1 1 Tf 28 0 obj In other,.! % NW obj In other words, compound propositions are those propositions contain! /Fontbbox [ -29 -960 1116 775 ] 1.277 0 Td ( logically ) Tj It either.! 0R^ % [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW _-VP... Qtoafav % ' b.5Tiloceqp @ + Tj It is either true or false but not both Tf Bp/HLJ... ` '? % c4 ( 5\QH $ Z\ ' # _-VP ` #! 28 0 obj In other words, compound propositions are those propositions that contain some connective In other,. Any statement, then which of the following is not a contradiction _-VP ` L7 &... 28 0 obj In other words, compound propositions are those propositions that contain some.... Tj ( or both! a contradiction? % c4 ( Q /f1 1 Tf Continue with Cookies! Or both! _Kb [ H p ) Tj ( or both! both. /F4 1 Tf BT Bp/HLJ ( B # ` Rp89W @ SEECPd/UmP8! % NW not.

Who Killed Lexie In The Likeness, Sea Of Thieves Map Size Comparison, Articles W