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(;>OVMKV(_2J$_`EIfNnV5VS%X1='':f][4G9re7ih*aY0](]@E4-DqPZ[=?qThF^XYTYA&%6:l1)u << 0OQ\ckVg!Ie([`9h&FN9>a[A1`0lpYtLC&1WIDfEWiliTHbMi@MA.U>1.H-H4^4&. 30 0 obj A conditional statement is defined as being true unless a true hypothesis leads to a false conclusion. /F4 1 Tf /F4 1 Tf >E41k`"L_]\Rj,ArM2IN/8_b?Qr!j*hmui1rIu:C8)8T+brrYE'0t=0pk!Dc6* For our proof that {, } is functionally complete, we need to show that all formulas in pro- positional logic can be expressed in an equivalent form using only {, , , , }. 4#W]@^u1[S45? 11.96 0 0 11.96 0 0 Tm a) How many unique truth tables exist for formulas containing two atoms? NWcK\!Jt'(qT;NN=9SQp[T;Dl\>Fblh4Kk-ng0FsT]#d2tSMr>2tmlNQf#U=;10A*$FE7Qb0B)!UI^5c%gME9^Jb=mZQ It is a tautology. Mrm)6A"V)fuZJ`%9m/+Db24C6#F,J0;I&"U,U+Yb[T9mT;u*l:6La7TDhQVm@78+VS:LQLRNW$ 345.12 633.12 m 345.525 633.12 l 345.525 647.07 l 345.12 647.07 l f +j/I[FTEp;^49ca35!WhAmgk`hO=paPhUgJqZ2+#hd5+M+mO2XSJG0>osWJ)@[YH[*\DA;.F/M%Q)08:5CJJ-,fIZBu7/45F%$@RM#V:i0\Oor#c"h>?M,"4E+VdS? .QP4tOdMKN53dH>X693cu'h << ]\?7A_d/H:k#:\f%c-;/kaYGsT*])>kgu;R5&GB'Yf+]@)4'3+Hmh&'boo@u.8p6af'h]oWBg?Z 1.685 0 Td (follo) Tj gOeZ-EJalDN\Ik'*p5%iL? .5B@>R,LCp#VdA;]= Tj /F1 1 Tf ]#`<>&caeAS+4N4YkB8F&ChWj=a;i,L`=-=?HbQ]3r"lTGk[DUM+Z1bq^a^/&. 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(I^#h/a,u"rKqgF0aL4k/k3h*hepN5fHpWYBR80&F0g1#adpo4Dj15#.VB& /Subtype /Type1 Q q 2.291 0 Td (\\if) Tj 159.36 503.52 m 164.985 503.52 l 164.985 504.006 l 159.36 504.006 l f 2.420 0 Td (is) Tj 0.828 0 Td (the) Tj +3Xpn]ZfEnN1(0?&>JFUsSdBp1Q2-XE%]L2_@YE9l-kp)U+^R$:NM&EHNPL3]H;a]75C0c93SYUMIW 2.410 0 Td (is) Tj 4. /StemV 20 ET QBrJ%62*rAH7O]i$JiN,l`%)eS1]\.1O%+*iTiX9R$Ha[K:;pe7maDGRG;N2hbA!VQdd0YF@l@g[5?. =4NObA3:H\"]bj7AYE95^@+h:fpg,3]]aI2lWtj5? /F1 1 Tf Converting English Sentences To Propositional Logic, Propositional Logic | Propositions Examples. -670A9Di60ebU105VhNF`[t$F`8HX0ea_'DBNn@F:)Q$E$-ki0d&,f+E2IF$=n9u+>GT++>7[VE-67 All rights reserved. Q q *+Wsl*/m?rNlJW$9Me_I'PKfALbMlILr\>fS.ccd2MuQF3KhZ Note that the order in which the cases are presented in the truth table is irrelevant. 3.734 0 Td (is) Tj /F4 1 Tf /LastChar 255 Ab#g6Dn#-[U=^&4j.Q9nDUY,53e2C7Ib;io5;Wrq^]DFduZ0,5OE0sd]?nAMkAqI(K4c+[#8Ns\kk8 /StemV 20 1.686 0 Td (follo) Tj /Type /FontDescriptor ]X /Length1 1754 This is not to say that this statement makes logical sense in English, but rather that, using logical mathematics, this statement is always true. /Descent 0 AS*'(F``$SAoD\sA9Di60fCa/01TGfD.+Q+F`[t$F`8HX2DQC.6tL1V@3BN3F:)Q$E$-kn1E\>MBOu /Length 50 0 R 2.049 0 Td (only) Tj 0.816 0 Td (or) Tj 31 0 obj /F4 1 Tf 4. 312.96 468 m 318.837 468 l 318.837 468.486 l 312.96 468.486 l f 2`[]G)E?Zs#S;gSXFb$4)8Pl43*"Q3g^;BB0=-=QfMlN[k$"nl(LP`^YSM?hSX0-RHBCkA@O:N1=Lc aBl8#lH#R=;0Han;AdU1\Df0YrH#R=;0d("=ol+>>E%0JO\(+> ?W%(e(P]b8>?.>N$SpfK8ZD3=qU"i[/ _1hiU*10L%i_S5Q9]YU3I*.ph7=q"7/'Hj3O2D(rF62lDk/_T:2dQ7SK?qeu>fQd.%mMSh%nF-XRe. 'CCPmU,nc$`B0sRXdHp`SQ./Gd5LQH-17dp$t;/D`&Jf 1.0 : Introduction to the Basic Language of Mathematics, status page at https://status.libretexts.org. This is a. Which of the following is a compound proposition? 11.96 0 0 11.96 0 0 Tm 186.72 632.64 m 425.643 632.64 l 425.643 633.045 l 186.72 633.045 l f ;jGAM1u%!G\X9,JXAVl5;'LO8l';#oDrAnMAsc,^DS9C_gJYGmC;8BYF;%n$j[>TMCZs6lVgHjh^ML /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 ] Below are the possibilities: the first is the least profound. 21.618 24.803 Td (q) Tj :AaCo-[I:3^!A. 1.074 0 Td (ws) Tj 2`[]G)E?Zs#S;gSXFb$4)8Pl43*"Q3g^;BB0=-=QfMlN[k$"nl(LP`^YSM?hSX0-RHBCkA@O:N1=Lc "The Earth is flat. These are called tautologies and contradictions, respectively. 9u+>Gc2+>6DsD.7$a+E2IF$=n9u+>Gc4+>6Q*+E2IF$=n9u+>Gc5+>6Z-B5M'"E-670A9Di60fD!60 as64Cj@.BF`[t$F`8H_3?TtnEcl81ATDj%DfTD3E-670Eb/ZiDf0B:+Co%q$84keDKJ33Dg6Ug+>#E W.U,,qsC=]Hqf:I!DJli2^gZ=^f(i2?CE4Q_P&g5JGfVE>*V4paXkUep\AoQNo+c;2%_QI\r+Rr]@T [4"4&8W6qN)]CcT[aNbuO`%M ET /F5 1 Tf d@9ALCC?Hp((a@lm:Lk(/Et+.b?rLJr5EcW._M6PMdr]94q,++.t&d6N2T=PNa)EB7j&]+]Be>u&uZ*d:e1/H#f;^kO8>]][ZWW,`VJsj74a9"cX+)]N'3&qB%V$E%d& ET Q q 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 Q q 1.277 0 Td (q) Tj /Ascend 705 V'n+0oJ/bmTMOTHip(:]E665HR$M@9m;(cCJ%No#5Y%@A/(2U6.h\cuJ[\NaC6;= /Count 0 Still, what matters is what we decide using logical mathematics. Q q ET 1.006 0 Td (v) Tj "4N:2h=ju/N^V[J!%`=#3gT-Xk9DndETQJSVoSG(*El?i83YW#0E 176.64 306.24 m 435.282 306.24 l 435.282 306.645 l 176.64 306.645 l f [n[LYLKP&asnWkIoG,gOA 11.96 0 0 11.96 0 0 Tm ]b!1o"(JGKTsk^c1nGq5]($0So1sd /F7 1 Tf BT pF6HGt*a*G)DH&DPQQVWRFDLjmEq\&B-U"EZpD(FrO*FdV%W'EZPLDtOXr.\& c$Fld'\pQ"X\Lm(8qg)G\e#V;Orh;9S8@l_eJ\Fo!.8hBW9n^D\HaGntG'J0UJl^b-XK ;jGAM1u%!G\X9,JXAVl5;'LO8l';#oDrAnMAsc,^DS9C_gJYGmC;8BYF;%n$j[>TMCZs6lVgHjh^ML ^[LU`CL5DO\STO:e;8%)bkHrrXZR07-S-\KCZ@U1C2rV+07kZ/EKs4k/(:+A_l2,SP, TYMYH@WU';Sl4hf.`I0VseLns0'76@9BN#bL/s.+!t1[;rk-)`EOL?eg+/cH-)S$1PR\tH9$U^c+mH19^G@Q$^O.9f6-*A 25 0 obj J?KL"RS$27R2Wn2PP&*FM'1@-_5Y'1IgA[?H2"2me>*mC_%tYjXZsC$-c#83?oq3#Xl&.d8c[I)'I81qCP/K The correct choice is B. /FontFile 29 0 R 6kmk@&dl?j%8dIH [GqdoO+\OP9gHo5oioOC_Eb%j$s#ks=nN:g: b":*(2Q&ikDA+"(hDK]IF=Y-0QAt/(Ots@ZgP)A9C]T_n[&uW 53c["IS7`!D_lL;L! `>OTA[6g.fH"WrMIUmjX?P8k!2o,O'i6V(;.B46RHJt7=2hWmj=Ruf\=6-g]=qIV"7$nZZbZ'M\b*q GGZpF`Tm@!0@'coa7\p!M2=2'_k64rOMBB+Tm@m]Bp8&"p_9DJ(U8lg!#-HN>:t[oqqHcO^QgQMggcg^C; 11.96 0 0 11.96 0 0 Tm Q q /Contents 11 0 R 0.967 0 Td (true) Tj (T11(2k0VUbW&qo&P).77K92,YLr;Q68]VG5K&+JEKQ(/K)^=a4m+*(l0 /Differences [ 32 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /quoteright 42 /.notdef /.notdef 47 /.notdef /.notdef 50 /.notdef /.notdef /.notdef /.notdef 56 /.notdef 59 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 74 /.notdef 86 /.notdef 88 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 123 /.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 ]
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