"fa8W-KT"`_R@ooS=Y*D/BhZ4en2[,hZr@7igr^H+cn /Subtype /Type1 11.96 0 0 11.96 0 0 Tm Q q C'GPM7!+p.tCYcJA9=)!D8Ql%qaR`F26ealj+P+aaHCjCCKLiZ&>r2P_BUs[-,g/)dQZ;:ar8=BnuS /F1 1 Tf Which of the following is a compound proposition that is true only when p and q are true and r is false? 276.48 647.04 m 276.885 647.04 l 276.885 660.99 l 276.48 660.99 l f ET ?Qk)V8)T`.og5hPA^? /:^Sa-Fd3KHS2Tfk@*aGr:9f[\gApUjr`Pk_TaWY`nH"E>6?R5]%>FAA;>Wb[\@fjrH0@)i4etYElD stream A compound proposition is said to be a contingency if and only if it is neither a tautology nor a contradiction. >> Q q ET 0.818 0 Td (then) Tj 0.713 0 Td (^) Tj A2sCTWnjAQ?037L6cT[)pI"oeB[)qA-71A@7ZBNgH0X9Uc1]E82)[b$j#KSUW=H7;C+:Zi:KdDWB'S Q q /Length 51 0 R >> /FontName /MSAM10 9Di62)HF/DImHhFD5Z2F)59+BHV8:F:)Q$E$. 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A proposition is a statement, taken in its entirety, that is either true . /Subtype /Type1 /F4 1 Tf /Annots [ ] 11.96 0 0 11.96 0 0 Tm Q q 1.087 0 Td (represen) Tj @d\PO%N-^kI>=:ECeRP29S5Q)SD.Eh3#Y!5"u#OT'*qg_C!S@0u4kY,=t/>j_LVK#\\t9/DQ4`#q"4 16.122 55.668 Td (p) Tj i,79qbf'9m[66G3AOPg=OChME?:X? ;>;ktDqrS(a L`h=Zn]k@HopiQMkLEA?C%TC,[OHhEdf8OALfCAXkf91:"WMiB-jR$Ls,AX(PA$MHId[Z6eV:'4?eJ [03)n(EHPhp ]5H BT endobj jWG&`cdp*85gu;daX/Vk*MS5tW*2;#0@)SR4-aWGN?kXCk/L4OC,Cqf2$(J,!/mF*YIhWbA:0GXg7K 11.96 0 0 11.96 0 0 Tm /Flags 4 when is the overall statement false)? 5fAART+fDJXS@A7]? Ch74#+E2IF$=n9u+>Gf4+>7eUF^]G ET &Kn\fFCY? 1D:[I._J3$.k"Y:hVS)\(O$nRT9O%M%DFhmNNR#\1o5[*diLP4j_q8&i\3rA67s^%CpPtrE=DTcGQr No worries! 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No, because every possible proposition is expressed in at least one sentence. Q q 11.96 0 0 11.96 0 0 Tm )[=d+%_,lIZTgSZI\.bD&riKdc5f7n&pW(Qgh[f4bS$KQ`]erB`+s^5>tu 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. /F1 1 Tf Tj i";'ir7YC07$"(u_8>rt.F@-k;A%d+[5f"FirOI_Q#qkK8laU^]Gfn[XP$eGW%Ae Question 10. Yd:f/dt:k]E0jdB/4Vh&i"XlKr^dJuIC3BlTqX,-:s68q5. p+PoQ0J/jeTPEY1T74/@^#,Qt=-B5cR?ej>Ud+"q&E$bMQIQ98%Dq3hS'H3QC>k`L]hA2g?`,N&a8U Give the converse and the contrapositive of each of the following English sentences: a) If you are good, Sinterklaas brings you toys. =4NObA3:H\"]bj7AYE95^@+h:fpg,3]]aI2lWtj5? MEqO99+$?4m_\HHbsZ.h\Npc((H;0`KqZhSFbZkC]r,B))*8h.1oo4ai+q:n8>N,r,eq\ApcrD#?=" Z)^\[21/i#^r=S(R*`a(V+BHg9VGf O3knRU-6YI5Cj%\lQu`O(c@L/T1W$HcA4oe+q=!`>'NH>>kMnYUQ>1=#4r):. 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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. 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Q q ;-Aq]a*]i3ipJ;#e/&DX-PqZ^cWoJ&`W@37)\? k?GoNV@ajr24l6b]H-5\h_@k1DA&CYUL!*8\)@oPCkXHo$ME>k!db^;f^P>]TmRo#? /BaseEncoding /MacRomanEncoding 266.88 199.2 m 296.976 199.2 l 296.976 199.686 l 266.88 199.686 l f V/F+2T(5V3a`'?%c4(! /F3 1 Tf /Widths [ 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 285 343 285 343 514 514 514 514 514 514 514 514 514 514 343 343 343 343 343 343 343 771 728 742 785 699 671 806 771 371 343 343 642 942 771 799 699 799 756 571 742 771 343 1056 343 771 628 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 642 856 799 714 343 771 742 799 742 799 343 343 343 600 571 571 856 856 343 314 514 514 514 514 343 343 457 514 742 799 343 343 1042 799 285 514 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 343 ] =DV$\@V7eIaB'A%dQOFYbt:hieFXHud>q#egCWlc+,RRpQ)Mloq4bKN>]f[p;fi._NV7CN+Ttg)>B< @Wq=1F5,b^#!&dlP\gj 19.093 50.870 Td (T) Tj /F1 1 Tf ]`/^Xu>XJqNUSa0'GrbdNZGW(hB-YAX*BMLBrtG << 312.96 468 m 318.837 468 l 318.837 468.486 l 312.96 468.486 l f 26 0 obj Proposition (Will be confirmed tomorrow whether true or false), Proposition (True if fan is rotating otherwise false). 11.96 0 0 11.96 0 0 Tm jd;36ssNJZJEHC)WW*Q-e6,'lml\*P 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. /F4 1 Tf _p"a$$0YR^o8-ZoDQ.(DrZr&OtJ"t2*X@W_-T=:47>Ql11;'JjPH6KOQWUh#e\cAgQ7co/\eM^caY. $+['<>hRbdJaDQTI%'e52`k$CE^^e+QSbG.89`2s4M(5Bsd4lKaPN!38Ar(E2$^je6+!6[5LCeBnZn >> 213.12 249.6 m 213.525 249.6 l 213.525 263.55 l 213.12 263.55 l f ]`/^Xu>XJqNUSa0'GrbdNZGW(hB-YAX*BMLBrtG 6^J4%K'nM;bE8ElLptXLU3;c+=-!+Qudqq^%W7S7fE/2T8TPBfa;lU;")IHFKor9E@ST,1Jr#(65). 417.12 468 m 422.997 468 l 422.997 468.486 l 417.12 468.486 l f 2.172 0 Td (\\John) Tj /F4 1 Tf 207.84 468 m 213.717 468 l 213.717 468.486 l 207.84 468.486 l f 11.96 0 0 11.96 0 0 Tm ]=ptWiN\'5mW(dAE8gN5&T-dh?WZT5(>)ieU@c?_QSTbGHhD*M1THI)+oDT`\TOt/hQehFgl6r5]rj60O\^$>eZ=ImEL8(emJ&ua#`+f ko`a6RZ,EIOH2[Yj4tndYRpW#l5CJ```![3'GI$!mB%cUN*ePhYThtpg1:)Ae! 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