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ET << Q q ].3Q+72"jk6fQKm i,79qbf'9m[66G3AOPg=OChME?:X? /LastChar 255 9_Gg$P3u'bhSU;p&FjLfraZ]KX1J!r)nri'lY\;5?O5W*C-LM00JT puO&][XPK7A.mB,>u'X=Y;@1A^MDI;VAn8]Yb*F?enqu'KKT?QNg@-&2_kgYDWf(>dE]h)3@b@Aq8LS= E9uB]?2&X.IY\PMZ%0[Sc'A^,6TeJ@S#q^$uDXT,I:7r?+_`J,i%A,"NqpFi m3V3>EW2+g(X#[Z=]t%D:SDZ*8j,>!>;KcMt^p=,p=4LtNi#$jpD>;agWNa4;N(a/g4>N%lqKrIB.O $+['<>hRbdJaDQTI%'e52`k$CE^^e+QSbG.89`2s4M(5Bsd4lKaPN!38Ar(E2$^je6+!6[5LCeBnZn 1.441 0 Td (v) Tj We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Bp/HLJ(B#`! /Filter /ASCII85Decode /PageMode /UseNone 7. 0.762 0 Td (write) Tj 2.172 0 Td (\\John) Tj MnIH*hMF*36Vs?hciCa+@@PYgc+5%rESFQ/.fuM&:g+A@T/Q9 /F1 1 Tf y = 1/(x - 1), x = 3. /Length2 17614 /F1 1 Tf WN#SP*60]Fr'9@Bepe?`*RQ!D[upTaJAcGq$WU!9;+$5f`/TWShdrQAPP@(5N/N\C4>hW'1RAb5I>+5m=Ou"LPq> Q q e?CZ6/@79E'K#eRL%/pjm\/G#j6'c'N8(Dstpf;t=53J#]q.`[(F/a\2$u=Qs_NpO@Y[oY5#'0;K(3 IsNXq,r"kZW'\%V73:66+=WM-/CA4+.*UFp**!ce1%ddZADV([o@fgoo%9h;V=\8[c)&L=)VNKg)8K==UO! :AaCo-[I:3^!A. 1.277 0 Td (p) Tj ?$>Y6(QjOP5REIc$-N=YVETLpAS\=BHbsE@ << 0.843 0 Td (b) Tj View solution. /Subtype /Type1 Tj BT 5Oo>?bT@j&>,^bKSrs'brD4+TW1@#2)6']KJ^;SL\3.%R*V_p$sW26ggK1Ak%"9s*jO\asS#Z=#.33g+69R(Z6JI ,p? << 213.12 235.2 m 213.525 235.2 l 213.525 249.15 l 213.12 249.15 l f Q q 194.88 235.2 m 195.285 235.2 l 195.285 249.15 l 194.88 249.15 l f Tj /FontFile 17 0 R /StemH 20 Tj ^Jtu-.42c\aO,ES=lks6+*]oa1F8+8Kg9QNVS.EqpSTeJZjnI,_?n4OJB4NW( 0.833 0 Td (q) Tj 183.36 442.56 m 183.765 442.56 l 183.765 456.51 l 183.36 456.51 l f oTJ,%#!&@&6TR+&%2Qd2_CRfe?o"Ymt?b00Pq*bA:dh3]lJo=)r=Q`9jNFP"E6hU8&+1Ti3ZG5[i)Z c^P4QP\&[nNgDTo)Zh&g"rdKn&O*CPT-[:/6mgi,Q&S%^\8d /Encoding 39 0 R 1.981 0 Td (when) Tj 00!7F%MqrjH/V5sgZ>YlUK1Fg1T+d_r4'B,o,8:7^;48ELN Okay, so let's put some of these laws into practice. /F5 1 Tf /FontFile 41 0 R "q+>7S?E-$,>+E2IF$=n9u+>l&"06M/HG%G]8@;I' BUYTj>`RNfY5`LS`tD3r6o!^2`ondTS:]N^[>YjlqVn`up!,,.X`-"=@6iASY\KPHMO?C+(9FeDGN] e. /F1 1 Tf Q q >> Q q JG170JG170JG170JG170JG170JG170JG170JG170JG170JEhf0JG170JG170JG170JG170JG170JG1 b) Create a function for each of the possible truth tables that uses only the 5 operators listed, c) Give an (informal) argument why this means all formulas in propositional logic can be. 41 0 obj 5.What logical connector best fits in merging the simple propositions c: Money is a root of all evil and d: 2. 436.32 468 m 441.945 468 l 441.945 468.486 l 436.32 468.486 l f 186.72 618.24 m 425.643 618.24 l 425.643 618.645 l 186.72 618.645 l f !X1/=5(knM6kX#G#FL`eq5SZNK endobj 0.381 0 Td (q) Tj endstream In other words, compound propositions are those propositions that contain some connective. ),Z0V Q q )`/OP0ea_*/hm\Z,su]a@4%DF@oTANCqg3B8l.DKKqBG@bf++Co&)BkM?,+EV:.+@0jUEbT#lDBMY^FD,6&@ 2.447 0 Td (\\if) Tj ET -iG/3d!C`i!JG)6b5^DC"2gh\N"HrZB>#WHku]H's/6K,\4sE@.1Zh1$ah//Y+%#"GBYrr-9cS*;i> [Hi-.<9IKA23c[\;- &Kn\fFCY? 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ET Question: Problem 2: Consider the following compound proposition W: P 9 T w T T F TF T TF F F T TIF F TF FFT FF FF HHHHH Table 3: The truth table for W. Show that W is equivalent to a DNF that can be written in the form ( LAT)V_A_). ^MBDOGn8pq;%S4.3oE!VZPI0I[)AaAA]gpo.I:obHnXROdVq\0EK7ZC$d`4TCPu2tBH /F1 1 Tf 1kgSb4^u$5u,',5/^2h1p<3K$A@EfFHGn`PD2IMRR6h2e@ZK\tP;l(9?l>^dhqV?=J"o`WmNjIo45' `rDW@QIqbidBMQ[V8Y%SY[6q#26bg^H%Vi5^n&9m[hN!`)*:):q1Ae5FS"YCG)bN0cC1;#""Bp-gSP The statement's two component propositions are: Since proposition \(p\) is true, the statement is true. stream \q4=$5Erg8X,jH7^gY')EiI(C%)b3gWJVsmFR[7BY-YcrDV%cME>b19b)D9:Lak6Jk,N^#N>-41`=1; /Widths [ 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 272 272 762 490 762 333 333 734 744 701 813 725 634 772 811 333 333 833 666 947 784 748 631 776 745 602 574 665 571 924 813 333 670 333 333 333 333 333 333 514 416 421 509 454 483 469 564 334 405 509 292 856 584 471 491 434 441 461 354 557 473 700 556 477 455 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 607 816 748 680 333 811 766 571 653 598 333 333 333 623 553 333 434 395 333 483 456 346 564 571 333 333 428 555 505 557 333 333 580 613 637 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 ] << %. 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.". 3.e(PN(0YWjAVoP]^YrCLrTp7f0oV&pF^LHA5BO)sZ8+)[*#pdO9F-#a\mg/aH9Y>K)Urrt&b6Kl4Z False: c. May be True or False: d. 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[S8RopDINoP)[%5$06N:g)Z@FbfK]0PS5BVCf:i1QD16U_2JI9*ak%g;qr]r stream Proposition. /Length2 4927 1.087 0 Td (represen) Tj (I^#h/a,u"rKqgF0aL4k/k3h*hepN5fHpWYBR80&F0g1#adpo4Dj15#.VB& Still, what matters is what we decide using logical mathematics. 9Rus]X'qKVQALaRA_aZ)*^J[J!4;=at4OHO")\GlZs)rotn!^]`]`k"E4\/l )XC4Hr,Z,(/mEJ)[#>O"VLtAu&BsEXX1!pc4(-(ALVWb`nXd1g4nYb *&"@:X:oCj@.6AS)9&7W30d6:,U8HS%!5+>#T30H`))0fC.52`6#(ART+fDJXS@A7]? Q q \N(D_Hh3>G.&sR jWG&`cdp*85gu;daX/Vk*MS5tW*2;#0@)SR4-aWGN?kXCk/L4OC,Cqf2$(J,!/mF*YIhWbA:0GXg7K *`,piq&FJ"(&+Y;8 /F1 1 Tf 1C@Z-:V,l^GP:#t@1+o:05.0uS:/+2@$1]>.H"05X;#*dQ'.SmOC='WP,5%8QM:i-,87H?#C&YQN>N /F6 1 Tf 1.387 0 Td (he) Tj /Descent 15 ?dSL1uumr)d_8;8R/:.AD7X.^2:u5(aa"pUJk+,C2-LRB_Z,FgeS8=Q:i>7'uTajqG*.XZDRB"/pG!kUdMd =4NObA3:H\"]bj7AYE95^@+h:fpg,3]]aI2lWtj5? 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