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The statement reads "2 is less than or equal to -3", or "\(2 < -3 \vee 2 = -3\)" and can be broken into two component propositions: Because propositions \(p\) and \(q\) are both false, the statement is false. JjH,t:W]g8rC41Btd"k"Lk9?K]i\Z9M?P"`mDL't4m Q q Q q /BaseFont /CMR9 << &x_1+ & &x_2+ & &x_3+ & &x_4 && =&0\\ @VFYq#Wl=gH]8 Q q 12.091 31.468 Td (Example) Tj 5Ch74#+E2IF$=n9u+?;A'04>uBF`[t$F`8H`3$9k`+E2IF$=n9u+? Xl*5#@A43SrlJd^DAmkbj\*1[j'H1&DHI6j+P"bf9"#_EH 1.278 0 Td (q) Tj 3DsHN#fMV=[D/ddlKFTGi`tpVH. ;O_Tm(_? 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ET /Annots [ ] Rule 1: The dot, wedge, horseshoe, and triple bar symbols must go between two statements (either simple or compound). h\e_Jg?JIW>tX]Lrn>o#kX=:k#K.B4.CHolj,daV]9B,Y0ds2gdu,"MCiHi$a;8c#SeFo=IYcEeE+- 1.441 0 Td (v) Tj c^P4QP\&[nNgDTo)Zh&g"rdKn&O*CPT-[:/6mgi,Q&S%^\8d The dual of a compound proposition that contains only the logical operators , , and is the compound proposition obtained by replacing each by , each by , each T by F, and each F by T. The dual of s is denoted by s. ]=ptWiN\'5mW(dAE8gN5&T-dh?WZT5(>)ieU@c?_QSTbGHhD*M1THI)+oDT`\TOt/hQehFgl6r5]rj60O\^$>eZ=ImEL8(emJ&ua#`+f /F3 1 Tf /Type /FontDescriptor 3.336 0 Td (is) Tj IJMs;=b70MVc&?;B.?PFPQ=o[?Xne:-?&8O.rdA/eK\Y4>. /F4 1 Tf [03)n(EHPhp << VONOkSGaF'R\;q@sd7;`CkBkX3jO.4u(nT&[$)N?unkDC`M2'Y7di'XY_i*-u^J1TCV9>O]-`dC%ocUh-!SpIr"$cRQB+8@slOV#KW :7&:J!lU($\a*M;= ?/8o4)N*VV$[$S"1Tr6-Pd@, Tj 11.96 0 0 11.96 0 0 Tm 25.622 37.692 Td (onse) Tj 3.695 0 Td (if) Tj Q q ET 11.96 0 0 11.96 0 0 Tm ]#`<>&caeAS+4N4YkB8F&ChWj=a;i,L`=-=?HbQ]3r"lTGk[DUM+Z1bq^a^/&. 0.713 0 Td (_) Tj 11.96 0 0 11.96 0 0 Tm /F4 1 Tf 1.650 0 Td (true.) /Type /Font 1.825 0 Td (,) Tj 273.12 414.24 m 273.525 414.24 l 273.525 428.19 l 273.12 428.19 l f LfCMb:$R[1;EM^Qk;A$pa/M*o"*[ Tji.Y=I-%R*>;R\N?\&rOnmm+oW$`56Z#+ir+B.f[#MEJtoRHH5DAiE038"EuP]Z%tMh4Ne@4J7!KJMUu8$n98CP"G4=i0+G.:us%!P*@hfNtrO1Y6tUrdD)3m5Ei. /F5 1 Tf Q ET Which of the following statement is true? _;!S/PV,`c=H=1noPi_56\JtLB-ZT\h]BBoLb5h"dVg(8h2AMO#f.HVdn"Ur[;WJK'[?9=!)<7XR;! Q q Q q Example: I will stop by to visit only if I have finished my homework. 3.045 0 Td (equiv) Tj [02Q( /Name /F6 [m[%-k.:s9nQC+9Z"(uj1L6o-3rm]\0enpg37aEF@,]_a]=qjMDWMGoOe;bDIAFfS/6aT.':\KPRHRdVfQ!RA1(s9j[!M`!l7! a5Z?".T6FWu2XXhf#NLjNHA[`YBEJ=E\QL+4(/IZj^"NWQ@0[4a6. Mail us on [emailprotected], to get more information about given services. X&h?b)gPD/==D6a]qt$bk\iffQqdeQgXngdek=*7n/6Vt(3'YG[Hh)QPStl%)"!M^B?.RGPET[mp>G 3n@;I&bDe!KmFEoJG,p5QnE-ZJo(@:X:oCj@.6AS)9&7W30d:18!N+>6Gf5ts'f+Co%q$854aBl8#lH# .4gU8g"H$@#8r\WTq@DTWB"b>cG3HT4o40L`?g#Nhk'. 5.225 0 Td (of) Tj << The symbolic form of "He is hard working but not going to win", is. /Length1 1754 ?1Ki=)4QnPJ>(9=$4+XDJI_B_m+-S8+5i0i(!EWOr+"%gR/I'Ca50HJTV endobj << 0.950 0 Td (ositive) Tj /F1 1 Tf prove that _______. +j/I[FTEp;^49ca35!WhAmgk`hO=paPhUgJqZ2+#hd5+M+mO2XSJG0>osWJ)@[YH[*\DA;.F/M%Q)08:5CJJ-,fIZBu7/45F%$@RM#V:i0\Oor#c"h>?M,"4E+VdS? 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ET /FontDescriptor 16 0 R Either x is not an even number or x is divisible by 3, but not both. /StemH 20 /F1 1 Tf 35 0 obj In propositional logic, there are two types of propositions-, Following kinds of statements are not propositions-, Following statements are not propositions-, Identify which of the following statements are propositions-. 4. r%:%PB(uC^!`1K(g2(iY7Q? [d0VObI-e$m#,fmlQph\!bn>JiA5%#N_FJd=AM\mNXn Q q Logically, we can see that if two lines are perpendicular, then they must intersect to form a right angle. nWD5]O]<3d/C=!kCpMgcHq)fq0! 51pIDp6FeOp(@a&VQSNg#q0oKUa#WadYu8!.OA3,o=^tOS4as)A6g[t&;iW>]q7)1>ZM#-K(XMO_CB << /BaseEncoding /MacRomanEncoding ZNb30:qBif^J>*8]6.Z\IcaY&.if*cid"R&pKk40J%q:sNFnX=70ZM[YFdH-HVb-T9XO@c7;otBpm] 1.250 0 Td (en) Tj /Type /Encoding 1.014 0 Td (the) Tj This is called the Principle of Explosion. -6m=(Gq! /Annots [ ] /F1 1 Tf /Name /F6 /Length2 18039 (8!QQO&01Dl7[MhH&*5GU`MT,%Y^bn+?`;6;-;EZ5:ij1NTfHj(!csp7=I19ARSAp@K0[Qags[Dd5Z \>.3b"_H+=ETC[Ia`G-UW]8]u0Rl"\r.q^*Xh'5d;GVl_bGVn6nZ.Xu#pu;==8bq>hU7FMh)LZ>Xqu;Qd*IEFbmp=_Cq$'uEf#K=K$g>I.MZU$il@%RR-RmnJTimmtX-Y>\%?qJFGM%1r[$Yad`rcJ9;)=O] Q q nn+AN=kc:W-\k3RoOuZ*I(sb]/FO NM!&HXuY2RSdahK,lgWA>dAS:*U4kN-U3F-QI?BasBm^,ZH43*)fl`B: The compound propositions p ~ q and p ^A -q have the same truth value when (a) P is true and q is true P is true and q is false: (c) p is false and q is true. ;RgBK"Efgb[X/H;ci]nj=p4b1R](@KHto6PdVMr98Q&&IQrkEpn:0DjY#c^$cmF1q[nP#,r4R, Types of Propositions- Atomic Proposition and Compound Proposition. EM)QC]19m<7!&! 20.982 0 Td (9) Tj /Encoding 35 0 R /Length3 532 BT /Type /Font 183.36 414.24 m 183.765 414.24 l 183.765 428.19 l 183.36 428.19 l f Note the following four basic ways to start with one or more propositions and use them to make a more elaborate compound statement. 1.424 0 Td (othesis) Tj [n[LYLKP&asnWkIoG,gOA 11.96 0 0 11.96 0 0 Tm 32.252 24.803 Td (\)) Tj *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? /Filter /ASCII85Decode endobj 3.687 0 Td (:) Tj ']\Ocg?_Epo(ESX0brlt)6Z-c,jjH? %ajo9FQmWC(AMh8aC? It is neither true nor false.b. 1.775 0 Td (c) Tj 15.223 21.205 Td (F) Tj Dg,Z/FD)e9F`[t$F`8H[0d&,XEcQ)BA7B@qBkM+$+E2IF$=n9u+>bnt04AmADg,`$Cgq=)BHV8:F:) '79>j2TCS(q\D1 26.502 44.974 Td (p) Tj $+['<>hRbdJaDQTI%'e52`k$CE^^e+QSbG.89`2s4M(5Bsd4lKaPN!38Ar(E2$^je6+!6[5LCeBnZn 3.679 0 Td (is) Tj Q q /Name /F5 _B%K$LDD9&q,;V?X,r0(b6s7?canlKJ8B'BmG&N#26/E*u&h7`n2&*Y/LfChE'!ga_j%sOQ7CO6AB#RlE 0,Togp6=[kgLIt$$>79EOaeX81Z,L%&1[GR[NItK;o4/U/-_q\dma-\2_emB3#7_Q*LqGMCn#iiL=k 11.96 0 0 11.96 0 0 Tm 26.187 47.790 Td (Logic.) ]hW:9(RpP/?Nm8\/(?.\kaA?oOFmpJ>+< J?KL"RS$27R2Wn2PP&*FM'1@-_5Y'1IgA[?H2"2me>*mC_%tYjXZsC$-c#83?oq3#Xl&.d8c[I)'I81qCP/K Q q @d\PO%N-^kI>=:ECeRP29S5Q)SD.Eh3#Y!5"u#OT'*qg_C!S@0u4kY,=t/>j_LVK#\\t9/DQ4`#q"4 P6>P$X0kAkjh?3X## /F4 1 Tf BUYTj>`RNfY5`LS`tD3r6o!^2`ondTS:]N^[>YjlqVn`up!,,.X`-"=@6iASY\KPHMO?C+(9FeDGN] &iQ:c*EftB`L*Pgnuf%$>uE$G*VU/Wnf;9dc;1r4;kWnA%"&/OMT9E>R2W1R1F*/g^T/Zs*fee2lsV ET oOT@^N"+dKeXkAG&e1Z7A[)gAa+(9OM?g(MVJKql+WNu8O2Hqo,fI9mnM;]Y\ehQIfX>e82QQo22+3*)_.SoF]V!2GS//Y0pI 'fp5E5,`pBC'G)n&mWH\?mg(3?m-0:%KtE=FhI"XAK'mEib@qO=+9HI9;u"P7Cjl@6A2s e?CZ6/@79E'K#eRL%/pjm\/G#j6'c'N8(Dstpf;t=53J#]q.`[(F/a\2$u=Qs_NpO@Y[oY5#'0;K(3 )F`[t$F`8H^1E\>B+E2IF$=n9u+?)/#02!F,F`[t$F`8H^2BXYH+E2IF$=n9u+? XP`:Xl:5I)!`7[3S^4Xr*h=72*(VAhs@8B-.H83T.S!#tai50sO*4Brku^U"(JuH+]Cm=-Jb5`0$V& -670A9Di60fD!603)t4Bl%^*+E2IF$=n9u+>Gc7+>6Q)BcqA;F:)Q$E$-ko0H`#FF(lb9F`[t$F`8H BT '2_9aDQAHJf3W#6sIW'r$Xm!,"e)HE4!Ti^NM,s!Q&s6ui-H_`>j4/)@lu!h+?/FoZ5iGrrXcUlZ"*psF&diHVYG`\SX'G7Xj puO&][XPK7A.mB,>u'X=Y;@1A^MDI;VAn8]Yb*F?enqu'KKT?QNg@-&2_kgYDWf(>dE]h)3@b@Aq8LS= V'n+0oJ/bmTMOTHip(:]E665HR$M@9m;(cCJ%No#5Y%@A/(2U6.h\cuJ[\NaC6;= This is an empirical statement for which there is evidence neither for nor against. 377.28 399.84 m 377.685 399.84 l 377.685 413.79 l 377.28 413.79 l f 434.88 264 m 435.285 264 l 435.285 277.95 l 434.88 277.95 l f Q q 16.848 24.803 Td (q) Tj "EW4CA(IqpG\YA43^,GuF@-MH(Bm3M :S"Jc*Yqo[Z56HV6;8IWdWN+HU ,p? /F1 1 Tf /3MIh#4UWGN^0W%:]WQu#"fhDDRVJL\u674ZjZ18/AEKKN: /F1 1 Tf @beq06Cl=Eb/j$Eb-A4F`[t$F`8H\1*A5hEb/`lA7]h#E eg`.%kFJ9hhA17@)NQ&:tCfl]q%V;Y]Fs$Z;i.-n8c9BSuuhq_[t1\J9MoXB9-So&/i=-p0JBlrn"- 26.859 33.770 Td (T) Tj /CapHeight 705 If x is an integer, then x 2 is a +ve integer. j8I;0hV\6E&hAh5(2c.O1($ZE`n4f4B"/K:NEQ"3L=ARFEZ=\Y5+S@f:YM%G1CXbFXCNYRb /F1 1 Tf << Once we know the basic statement types and their truth tables, we can derive the truth tables of more elaborate compound statements. o%q$84hc@rGmlDJ((I2)ZRcEcPT6$8, V1hT8al-@Uk^gL >> /Type /Font HcgL^LhRJDnTLG4+FdWM^GZt5EWm$71TY@H``\>r/h2t#O=+;7#D,n%":,P a*GPoge2ebfl5`k_m]1HnRr_.Y,D]dULX,QACV=QcMqA7QXd$o 19.174 23.604 Td (T) Tj 2X;%m?9OPj9B5-1\0nGEdD`IkZTk5D4at'X*i(V&NJ&M,>. ."[X3\JNuB_jK0j%!Z4cpKo,R*KE1Mn\!?Pt^$-s3(jQrED!V;2^e+1lP/.=. ?G*c%4Q:O8-2]dE1,JnRem^eqkW8tupos*!VZ3$cbdbG^Z#Q&Qt)B Below is the truth table for the proposition, not p or (p and q). 11.96 0 0 11.96 0 0 Tm /Encoding 23 0 R -26.481 -1.166 Td (equiv) Tj '&BRL 0.771 0 Td (is) Tj Certain types of proposition will play a special role in our further work with logic. /F4 1 Tf !/%Y1rC6(P(4;tos1?qZd!Z"`LD])VVL$"D&jP:$L2:n;Pj3%R)@#HW1DY\hTe4Qdb5An_\QFP'YZ/l9pgUJ"NE5\=!J/Pi;I:r !0`V3.O]ZiqrjU3.pD`$!t''NH5`6!msX)7,)uE;m0DAg0X?G_/[Hmo1Mc/IP_G1V@YB9nn$E[ijW+ 11.96 0 0 11.96 0 0 Tm /F1 1 Tf << f0D7GEFF]O!'#E6GU8Tf,5:MLAR6Y$eOs-,VKgt,KtbCC0%+Wf0!r:rZ%c;H4ef-VFNF`r)*! jVWdGL\[W\#AluEM'U=Wc2rAa_o!-RjM.A9o]q/aL#A /F5 1 Tf /Contents 7 0 R endobj /F5 1 Tf 434.88 292.32 m 435.285 292.32 l 435.285 306.27 l 434.88 306.27 l f >. 21.050 34.969 Td (T) Tj 21.316 54.468 Td (T) Tj U4BT@jtQ/**,iYR*1aE\UcNjGlK=]XC+.=>Po][mX60fC']@fr,0,`b],*Q.c5:kn&LpL-u9K(#=]" ']\Ocg?_Epo(ESX0brlt)6Z-c,jjH? 2.288 0 Td (John) Tj /F1 1 Tf (T11(2k0VUbW&qo&P).77K92,YLr;Q68]VG5K&+JEKQ(/K)^=a4m+*(l0 201.6 442.56 m 202.005 442.56 l 202.005 456.51 l 201.6 456.51 l f /F4 1 Tf HY$jplK#s#:k?$f? /F5 1 Tf \YE7Kfr-C:,OjcFh>LIh%,5eW[E?^`^=2.k1Q:A++9fD$PF%&^msD9$<6/qg;1R+&6%01aOh7/-5JR >> 1kgSb4^u$5u,',5/^2h1p<3K$A@EfFHGn`PD2IMRR6h2e@ZK\tP;l(9?l>^dhqV?=J"o`WmNjIo45' To gain better understanding about Propositions. NM!&HXuY2RSdahK,lgWA>dAS:*U4kN-U3F-QI?BasBm^,ZH43*)fl`B: 1.006 0 Td (v) Tj "^8I2pIgV+sbp^o 3.799 0 Td (.) E^jI'>i)XnMfK2B'g"(=\! (Here the connector "and" was used to create a new statement). Q q _.R&nqk&G@MD*g? -28.927 -1.166 Td (John) Tj V$0TNq%rN'+)72e*4l4lC$0j7ll>p$E2F/]7;EW$j/C9om%^?>3`\"Sm8C1cXQ-[6c9;Ep&*NFuDE))Y81V8CdM]f]Z?he#Ho]#Dd_#,-mb+/ce"'SA)p%-?WXnOU9GNjP1Wbh&,=EG:Yp&k4V+ZI_S%73?k< 1.277 0 Td (q) Tj 4.079 0 Td (is) Tj K(G'3gER/!JL^^SWC,G]%iZJgk(Qq736B_1"6?R@fldOj9cK_Rflms!2!j6_k>O>5_5Z2=lIJ>X7Mc ET *tgsHY6bB!WPLLI/0o3)Q5s./r$ae)UL*@jV?NkHt^[P6]N_8M0 /FontBBox [ -39 -250 1036 750 ] /F1 1 Tf 2.229 0 Td (alen) Tj \$@s=c[0K%H3(Uig80fl]mEnH1\T&SqZf,7e!>?$*!0`8#9dGldR#(-HbP@5o&.7+^W8L(jJujQ/G&dhn )F.WY&h(qI/'UPI9--nLU5`;RE@S,Q\UI9KcegVKd>%lLr]fCW7tY)YWfPols6nPfif;b3Qe>>M "+KS9V$:$eS_9. 165.12 442.56 m 447.234 442.56 l 447.234 442.965 l 165.12 442.965 l f ! V ; 2^e+1lP/.= endobj 3.687 0 Td ( true. & nqk g!? Pt^ $ -s3 ( jQrED! 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