which of the following is a compound proposition?

qA9=,JL19icGY4.XN>W_170MYHr2H+O(N=(u6@Sem!77re*ELWh=!(Z:'Lh"m.QH6`t5]_OBkHIcd*4`a#Q$'pf/s! /LastChar 255 You can see that the negation of a proposition affects only the proposition itself, not any other assumptions. ET JjH,t:W]g8rC41Btd"k"Lk9?K]i\Z9M?P"`mDL't4m 204.96 661.44 m 205.365 661.44 l 205.365 675.39 l 204.96 675.39 l f .4gU8g"H$@#8r\WTq@DTWB"b>cG3HT4o40L`?g#Nhk'. 4.241 0 Td (ma) Tj pgih4+`/->MP>u7juZK%au0%^AXT>&OW 11.96 0 0 11.96 0 0 Tm 24.495 50.204 Td (is) Tj 11.96 0 0 11.96 0 0 Tm 2.629 0 Td (e.) Tj 186.24 604.32 m 186.645 604.32 l 186.645 618.27 l 186.24 618.27 l f ad$][G%agN7Od_AD(>'43kAi+_,Ml#61]mAY9g0=r6(,Wul0e0m8`tH?5EBO]G/Gq58u>kP /StemH 20 165.12 399.36 m 447.234 399.36 l 447.234 399.765 l 165.12 399.765 l f 33.545 50.870 Td (T) Tj l9&*Pg.2:tQ/"&:;4a0(a\qh-&,oN_lR:(_.R708/c,OXf(_!R%mp[TJRPPXs%;ja*1%=s@JNR/4&Y [LdIg Q q ET 5N7. u]*D;TS+S%XFhrtc,Xs7^pmVN"2@hMC)VBkmKCAs[o@ 0.769 0 Td (!) /ItalicAngle -14 e?CZ6/@79E'K#eRL%/pjm\/G#j6'c'N8(Dstpf;t=53J#]q.`[(F/a\2$u=Qs_NpO@Y[oY5#'0;K(3 11.96 0 0 11.96 0 0 Tm :r Discussion One of the important techniques used in proving theorems is to replace, or sub-stitute, one proposition by another one that is equivalent to it. ?1Ki=)4QnPJ>(9=$4+XDJI_B_m+-S8+5i0i(!EWOr+"%gR/I'Ca50HJTV *NS.ft#YQl`I4haq'$-p:$hn@;?p7Ao92\!NT0R?0F?g5Jn!C^[CqIW"T/;(a7oK_RL?G]+"i6H"Q4>:;-d`q\O(8V66:UR"EK@S? n]dTr)B;Zkq'D8?:Ii0n3opdh+`F;QjnJB@Nn!*e\qOH4WU5[ag++l-neU6? E:SZo,G16u5? 8H^3$9kL+E2IF$=n9u+? Q q /F1 1 Tf )`/O..3NYB@:X:oCj@.6AS)9&:2b5g@q?c26Z6phEbT0"Fo(@:X:oCj@.6AS)9&7W30d:18!N+>6)V;cth/+Co%q$854 t'gPXEif6:uUJ'#-#Ne!nE?$5M=Zk2=-`j,+"DPZf:i. 1.985 0 Td (ositions) Tj Mrm)6A"V)fuZJ`%9m/+Db24C6#F,J0;I&"U,U+Yb[T9mT;u*l:6La7TDhQVm@78+VS:LQLRNW$ endobj Q q endobj /F1 1 Tf BT :j3jUJ1fO\IX/%0>a&D7gMX[f.EU79& 32.641 55.668 Td (p) Tj \4$)\mqWb&r1)kOTiFuQ,ij0jhCY!:ggY_=ndG'V;ZmCHn(U:?.cW'dDWK+d/>VFC&? MEqO99+$?4m_\HHbsZ.h\Npc((H;0`KqZhSFbZkC]r,B))*8h.1oo4ai+q:n8>N,r,eq\ApcrD#?=" 41 0 obj /FontFile 33 0 R \$@s=c[0K%H3(Uig80fl]mEnH1\T&SqZf,7e!>?$*!0`8#9dGldR#(-HbP@5o&.7+^W8L(jJujQ/G&dhn 32.703 37.368 Td (F) Tj 2.311 0 Td (Illinois) Tj /F4 1 Tf .>ET+1/-;cL8&E@ZihJOk7\=S6Zu4bdi*GQr,SnH,L;_6h_@1lCXY!+Ou$=QV'=s]Z8EOZ`UW=S><6p]ZRcu:U?6,sY+,,0(kM*8@e,P/#ApUh_$>OlN(Hpja\R ,5V9M0V"@cmC%i76=gh*Vs8p&m:Yb*W/rkG`^9;n/@J5t*Wh3sfI)_T[DQD'Le;u5p?MDQ)RLHgVJWWaET4hC%H.="85d)pc,CSY 1.057 0 Td (from) Tj /Contents 9 0 R Q q Fbj/GY2Gm2cQTUe0GVHHc0-%0peL5tIV:U5/2$,T*cpRIYH+9t04R /Length3 532 2.406 0 Td (is) Tj 0.959 0 Td (false.) 2.230 0 Td (the) Tj In other words, if it is Friday and the students take a test, then {eq}p\leftrightarrow q {/eq} is true . /ItalicAngle 0 /gDWDqR'K(<7LNlRCYRkTAGQ^Br[n6dQ%i^/qY'#!63PM_ZBh?a1$K8]Dqns7HmYVSH)$07+hKRhI: << /Length 50 0 R The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. 2.474 0 Td (truth) Tj nca2ne:O'lhYlM%Sp+k2.7i,3eRUOK/Of*.OeGXK6XF(W>0ee*G(4gVjVKj@lKQ%Y0%AOm:[5O-9p`k2(*"-^l5 KR3=7&T6Z6phEbT0"F^/he^sEb/ZiDf0B:+Co%q$85.mFD55r+=KTqE-ZJ=ol+>>E%0JO\(+>@(DEb/ZiDf0B:+C 11.96 0 0 11.96 0 0 Tm 35.278 45.872 Td (then) Tj *\UE[m1X?ZsYeN+,eu#iLQFUtRB;`]";jcKLN#n1na3h].NCR'?6jc;'q:1PF'"^o8q"8suGf-Nko( Formula: a b = a b. BT 19.127 53.269 Td (F) Tj BT H[B?BGIpq>^nV&.r:J:_E!V]AckS_0!7'Je. /gDWDqR'K(<7LNlRCYRkTAGQ^Br[n6dQ%i^/qY'#!63PM_ZBh?a1$K8]Dqns7HmYVSH)$07+hKRhI: \(\neg p\) is "not \(p\)," or the negation of statement \(p\). ET Q q BT 2`[]G)E?Zs#S;gSXFb$4)8Pl43*"Q3g^;BB0=-=QfMlN[k$"nl(LP`^YSM?hSX0-RHBCkA@O:N1=Lc 6_,/Q(jD,qb\*-^4]Z8lB?XA!.`Up8W)M^o_8X7(8%bU#shr07*r%p.GZ3JH:OLl#_Zs*O/#PV<7i- mCf+,Q3%#jjK8@KZZ;$0UGY>:C!IEp#]3Utdi>5`&MGg_sVWb.DY%"5RN&&,@R&q,*qqcAhWT%r1[R/TYD ])+[9k<7b"Qls"1^8% endobj 1.285 0 Td (the) Tj ET Which of the following are correct ways of determining if two compound propositions p and q are equivalent. d@9ALCC?Hp((a@lm:Lk(/Et+.b?rLJr5EcW._M6PMdr]94q,++.t&d6N2T=PNa)EB7j&]+]Be>u&uZ*d:e1/H#f;^kO8>]][ZWW,`VJsj74a9"cX+)]N'3&qB%V$E%d& 1.006 0 Td (a) Tj C'GPM7!+p.tCYcJA9=)!D8Ql%qaR`F26ealj+P+aaHCjCCKLiZ&>r2P_BUs[-,g/)dQZ;:ar8=BnuS In propositional logic, propositions are the statements that are either true or false but not both. /FontName /MSAM10 >> TYMYH@WU';Sl4hf.`I0VseLns0'76@9BN#bL/s.+!t1[;rk-)`EOL?eg+/cH-)S$1PR\tH9$U^c+mH19^G@Q$^O.9f6-*A Q q >b25..4"!d#! 1.985 0 Td (osition) Tj C!S'[A^?k1)'Q&Iud&lPe#,([:Tb"[t8doe`7g)0eW8B4oV7o@-XA$qGWPG\X1"0f^QX6.,OE<2p7D Below are the possibilities: the first is the least profound. >> FPcOTa$A6n"V\L[El$0 e;lB^?IcS3Tb6+hu77o7hSpQ2bO*E$NMo?uuM?_P$*QS@sgOArG-6cf7%7:V! Q q Truth tables are more useful in describing the possible truth values for various compound propositions. 21.350 53.269 Td (F) Tj /F1 1 Tf @(DEb/ZiDf0B:+Co%q$84hc@rGmlDJ((I2)ZRcEcPT6$8Pf3+F>gcBl7HmGT^RB@qZuGc/+>7SGDKU"CE-670A9Di60fCd005tKCBl@NlASuU$Eb/c(E-670A9D /F1 1 Tf /F1 1 Tf f7+>7eEFD5f.Bk;?.E-670A9Di60fUj004\O. ]Pf[nTEhIMh4='dBX@uBNe?JSG=S68Hdi'0`rH` 446.88 399.84 m 447.285 399.84 l 447.285 413.79 l 446.88 413.79 l f 2.583 0 Td (v) Tj 8fW5$IIQ;(\*l+((@H=P#d:SekbK0#t2p-J$>2^V/&S;i Right on! 1.278 0 Td (q) Tj 40 0 obj Q q +E2IF$=n9u+?2/"02j!4F`[t$F`8H_1a"GN+E2IF$=n9u+?25$03'-6F`[t$F`8H_2]sbT+E2IF$=n 14 0 obj 20.367 38.568 Td (p) Tj Z&7+I4iFj)1-6XQFM,tnFqYF>6hD!&/!BlUg9SDR-HnfZa3Uc]eH%S[%d)h%i]@=+8fiWZaUCIu>'# $*21&CR:u=p;&c.>&AW_hf+N cmKWl10.\:n3`^Slq=Yc"FMG";>MMTNY>r$aT>R,-]I/pXAi`mZBB!3ca_;7N^$Ig-KD2Y]ES7%P9chjrr4e"s9X'5g?b6L^MJqK7O3O-p$FQMnZT>b)lH R=;0Han;AdU1\Df0YrH#R=;0d("=ol+>>E%0JO\(+>@(DEb/Zi nm5p33R*%j9sVNP:C]*b&crr(d'b,WjC>neG9'E:)ZfO$M+\if+#J'L9[-MfQ. hdk5]Yap"ZReWN5?O(mk$Qk;[,D:ts%ap4[NbX]\X`9s+dKbNr,F^eHBeH1DYO2H12>ij^K@? MEqO99+$?4m_\HHbsZ.h\Npc((H;0`KqZhSFbZkC]r,B))*8h.1oo4ai+q:n8>N,r,eq\ApcrD#?=" 18.862 34.969 Td (F) Tj 75@De!R,Bldi.E-670A9Di60fLd/04Aa?Bk(st@r$:&F(HJ5F`[t$F`8HX2`)X1BOPq#Df9N6BkM+$ 11.96 0 0 11.96 0 0 Tm A->10mRJ8.lFRP](G.e5T)/f7-_aBN/.dtBP1du5/k" 11.96 0 0 11.96 0 0 Tm 38 0 obj KAL=@or*j^@VdX/HabK-0iJ1.G'op#6[60)7?=cn6CQ=K@P"%HH>-)sb!.GEWM0EV,->9iGJ;$cVO\0uK*2c /CapHeight 705 a. 2.200 0 Td (that) Tj Mathematics may be interesting for some people or may not be interesting for some people. 0.713 0 Td (^) Tj ]*qHJ'8=C!pHFL)Pk+s&/Uo4T]f)?QO"kW]k 9u+>l,$04Sp:Df-\:F`[t$F`8H]2'=Pu,#01$e#F`[t$F`8H]2]sb@+E2IF$=n9u+ Q4'_O.%X\!]!U?Y')T;"oMX3d>O5TqO;[`$5[VS? 2.340 0 Td (prop) Tj 7 0 obj /Outlines 2 0 R /F4 1 Tf ET :po47o87']?7\=9hXR?M7=S(U2AKlI[J+8-c1GcB*Ms".NC\rOqqS_0k>HWtnRTKm8N 4.980 0 Td (prop) Tj ET Fb%M^Y'Om(j$u:BQ9(ES`,CW>pMd>F_>-'(V5]a#n,\?Y@JjYQVBG@(pLLA`T:$I"amn(\RjEMF')& &x_1+ & &x_2+ & &x_3+ & &x_4 && =&0\\ /Type /Font /F5 1 Tf Q q /MediaBox [ 0 0 612 792 ] 2.479 0 Td (is) Tj /ItalicAngle -14 ?c2=2KpCGQ/6F-)lLY&(/;=6NGJLPCVqEfuWWLn1PYsZ0'/>%^#L"l5@JI!X\3[*-*p>X False: c. May be True or False: d. Can't say: View Answer Report Discuss Too . 11.96 0 0 11.96 0 0 Tm ;JmO9 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. 3n@;I&bDe!KmFEoJG,p5QnE-ZJo(@:X:oCj@.6AS)9&7W30d:18!N+>6Gf5ts'f+Co%q$854aBl8#lH# H=K]EOt>HU",L\,C3\fmPlSm6VT?0oV5EXp7:s;pc6@d%Q(#>N*a59uupb1EuhCUYQ`p(l=,_)PLUqe& BT f]4RkK"2hC. 0.747 0 Td (!) )F.WY&h(qI/'UPI9--nLU5`;RE@S,Q\UI9KcegVKd>%lLr]fCW7tY)YWfPols6nPfif;b3Qe>>M 229.44 672.48 m 235.317 672.48 l 235.317 672.966 l 229.44 672.966 l f :S"Jc*Yqo[Z56HV6;8IWdWN+HU Q(+>759Bl%L$B5D-kFGT++>7bDA8,O^C`m\>F: ]gJd]PPOGjD3^B]@ BT %f:+f`1O`&nq-i /FirstChar 0 endobj I=2JJf4GPD_i/KXH;(AFKL\'$VHh&Gj$g`AjZUm%r@&]XV34Lj`]*t9\Z_tJFL^Si4`phc54K2cB"h /F1 1 Tf /Differences [ 32 /.notdef /arrowright /arrowup /.notdef /arrowboth /.notdef /.notdef /.notdef /.notdef /arrowdblright /.notdef /.notdef /arrowdblboth /.notdef /.notdef /.notdef /.notdef /infinity /element /.notdef /triangle /.notdef /negationslash /mapsto /universal /existential /.notdef /emptyset /.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 /union /intersection /.notdef /logicaland /logicalor /.notdef /.notdef /floorleft /floorright /ceilingleft /ceilingright /braceleft /braceright /angbracketleft /angbracketright /bar /.notdef /.notdef /.notdef /.notdef /.notdef /radical /.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 /minus /periodcentered /multiply /asteriskmath /.notdef /diamondmath /plusminus /minusplus /circleplus /circleminus /.notdef /.notdef 174 /circledivide /.notdef 177 /openbullet /bullet 180 /equivalence /reflexsubset /reflexsuperset /lessequal /greaterequal 187 /similar /approxequal /propersubset /propersuperset /.notdef /.notdef /.notdef /follows /arrowleft /.notdef 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 ] /StemV 20 These are called tautologies and contradictions, respectively. endobj 1.985 0 Td (ositions) Tj ?1\WOrcEm2aA?tJqB5"X\Cdu_J/3TX8Yfe&"BQ6-03;JDuZfAGYO"sQqDX &Kn\fFCY? 0.862 0 Td (op) Tj Q q Q q 1.686 0 Td (c) Tj *g@AdBQNF6SH*tpbFp2$%NNeD$`Q9agmAC/e4 13.310 41.540 Td (q) Tj /Differences [ 32 /.notdef 34 /quotedblright /.notdef /.notdef 38 /.notdef /quoteright 42 /.notdef 60 /.notdef 62 /.notdef 89 /.notdef /.notdef 92 /quotedblleft 94 /.notdef /.notdef /quoteleft 123 /endash /emdash /.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 /Omega /ff /fi /fl /ffi /ffl 180 /dotlessj /grave /acute /caron /breve /macron 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 ] go9!kHG=oC;uJr:u8( 28.103 16.119 Td (q) Tj ET .1E\D.1GL",0JG;2Eb/ZiDf0B:+Co%q$85CsBlS9,=BH\'0JbFD3&)OdAS)9ZF`MM6DKKE'@rri)DI Examples of Propositions. /Length3 532 1.981 0 Td (when) Tj p@n:kpib6utY@QpN@&jC-&V[T*lVp#i[+ChPD"LEV)TPJ6nMN' << Quality 1.985 0 Td (osition) Tj 395.04 249.6 m 395.445 249.6 l 395.445 263.55 l 395.04 263.55 l f .1E\D.1GL",0JG;2Eb/ZiDf0B:+Co%q$85CsBlS9,=BH\'0JbFD3&)OdAS)9ZF`MM6DKKE'@rri)DI !FIjm<6SNEKF\`,eQW;ND#aNuh J?KL"RS$27R2Wn2PP&*FM'1@-_5Y'1IgA[?H2"2me>*mC_%tYjXZsC$-c#83?oq3#Xl&.d8c[I)'I81qCP/K 11.96 0 0 11.96 0 0 Tm oTJ,%#!&@&6TR+&%2Qd2_CRfe?o"Ymt?b00Pq*bA:dh3]lJo=)r=Q`9jNFP"E6hU8&+1Ti3ZG5[i)Z &G=lJ, 4UWGN^0W%:]WQu#"fhDDRVJL\u674ZjZ18/AEKKN: 1.042 0 Td (from) Tj /Encoding 27 0 R Q q Proposition is a declarative statement declaring some fact. 9u+?;A'04>uBF`[t$F`8H`3$9k`+E2IF$=n9u+? ]#`<>&caeAS+4N4YkB8F&ChWj=a;i,L`=-=?HbQ]3r"lTGk[DUM+Z1bq^a^/&. ]_=WC@&NZK:JU4O&' /F1 1 Tf 14.35 0 0 14.35 0 0 Tm 1.342 0 Td (exclusive) Tj endobj +>77JE-670A9Di60eb=)04c8FF`[t$F`8HX0JXb(Afu&8F:)Q$E$-kh1E\>`+E2IF$=n9u+>GQ,+>7 11.96 0 0 11.96 0 0 Tm ?.bo1O-3t\C/tQ%gB y = 1/(x - 1), x = 3. << 0.914 0 Td (\264) Tj 1.899 0 Td (p) Tj -2.185 -2.770 Td (1.1.2.) %^h!@Wq7dq?,\kiDs_^jR/&DZf/? i";'ir7YC07$"(u_8>rt.F@-k;A%d+[5f"FirOI_Q#qkK8laU^]Gfn[XP$eGW%Ae Since \(2 \ne 3\), it does not matter if \(5 = 2\) is true or not, the conditional statement as a whole is true. /FontName /CMSY10 C!S'[A^?k1)'Q&Iud&lPe#,([:Tb"[t8doe`7g)0eW8B4oV7o@-XA$qGWPG\X1"0f^QX6.,OE<2p7D 11.96 0 0 11.96 0 0 Tm 0.957 0 Td (ouse) Tj 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+> p&YF'i5C;M(##F')5#E^14VZNUk.IL/*\s>Z/+f,?bNdD:W 0JG170JG170JG170JG170JG170JG170JG170JG170JG170JG170JG170FBKf0JG170JG170JG170JG 7!Uhh2.E#+9(/>5O5>@M1e5P;i&GB`Unr(nK7n_SPih/FXBXL1XQT/3"#+71\\8HWQ!>:e:AOVAL[j2/Bk/hM@gfQ"NE_aKqbrU,pHli*7i/q'113MM$6'YqjnacJ*,M! /Descent 0 :e#u)eL/WTjUbR$[=]K.00mS5*C`>ant.8dIpP*<2BTGXegDUT7q^7C\B7T3,mu# 0.959 0 Td (true) Tj /Type /FontDescriptor 0.558 0 Td (or) Tj ?c2=2KpCGQ/6F-)lLY&(/;=6NGJLPCVqEfuWWLn1PYsZ0'/>%^#L"l5@JI!X\3[*-*p>X 11.96 0 0 11.96 0 0 Tm Q q \q4=$5Erg8X,jH7^gY')EiI(C%)b3gWJVsmFR[7BY-YcrDV%cME>b19b)D9:Lak6Jk,N^#N>-41`=1; 51pIDp6FeOp(@a&VQSNg#q0oKUa#WadYu8!.OA3,o=^tOS4as)A6g[t&;iW>]q7)1>ZM#-K(XMO_CB [f Q q 1.798 0 Td (the) Tj ?.bo1O-3t\C/tQ%gB $[qF`M"Y`WeHQ`:j@Q\Tr=3ThR9uMudA;^^._uA8s!0m[T0%5Hcu'FjI@k)V=$Z #O"kTYFT5K\d533\qeX/>R&;mQNWb4TN`Vs'(c!1-mWHs5@m^VY=9DdRX_VMF)FT8_i nWD5]O]<3d/C=!kCpMgcHq)fq0! BT BT 2.099 0 Td (ositiv) Tj ?Tl%E")uOUmHu!.%tR@M@Wep0C!m.CLgjA6Wu.g&Dk&K5ohsKU>e0A9 (lJR2X&q=Z/"&f9&\+)=kI7E0gX3STi9$JJ;'*Nsj:>h=_ P:9X'P6+^,Br>rEFbC.3hT\PI-0;f4NG/m\q@Be' bZJTE""!C4HD8bS3[)$6nNM[+@b;^bqq"Y5 3.825 0 Td (then) Tj Convert from symbolic notation to words: Q q $22CHtWp[e[V/mp-BEq^qTjX[ZAi=4:dM_TYc98Q&3T[Mg',p9V_9G-I06E::IiP,l0kb+[N/Rs'FWftnR>AV7#9r\pu=O#i7W2ALo9-uE! /F4 1 Tf g]q(Z"T,/%.MIC)J,,b&k/?=^"lom50f-dNXdY[_?1Cs;cML9)?=YGBfJ6=F:_HDT(tKf&IU"cjl6> /BaseFont /MSAM10 /F1 1 Tf @rj[1PCe3ng,A2%DIQ&J!QG_.R^e+RC(*U#4RSTh#29o%22*jnGg*drpnK.:hbhX.DgIN*@.N9qQT? [03)n(EHPhp 0.408 0 Td (hec) Tj /FontDescriptor 40 0 R Tj !jh1H15[MWo$uD""=r''lsC_TXW*^A.?ERn. d. No, because propositions aren't contained in sentences at all. /F1 1 Tf ;jGAM1u%!G\X9,JXAVl5;'LO8l';#oDrAnMAsc,^DS9C_gJYGmC;8BYF;%n$j[>TMCZs6lVgHjh^ML [m[%-k.:s9nQC+9Z"(uj1L6o-3rm]\0enpg37aEF@,]_a]=qjMDWMGoOe;bDIAFfS/6aT.':\KPRHRdVfQ!RA1(s9j[!M`!l7! Nn@F:)Q$E$..r+>7GHFCfK6ARfgrDf-\:F`[t$F`8H`1a"GfDeEco@;K@iA0>i6F:)Q$E$..u+>7PL 1.985 0 Td (o-) Tj 39 0 obj t]'a-Pn6,7\WN]=i_kKH8@p0@qLbMlL#? What appropriate tool is applicable if the population is normal, sample standard deviation is known, and, Access to our library of course-specific study resources, Up to 40 questions to ask our expert tutors, Unlimited access to our textbook solutions and explanations. 2.446 0 Td (ositions.) Q q /Type /Outlines /Flags 4 _p"a$$0YR^o8-ZoDQ.(DrZr&OtJ"t2*X@W_-T=:47>Ql11;'JjPH6KOQWUh#e\cAgQ7co/\eM^caY. 311.04 647.04 m 311.445 647.04 l 311.445 660.99 l 311.04 660.99 l f Q q 2.464 0 Td (is) Tj 11.96 0 0 11.96 0 0 Tm ]b!1o"(JGKTsk^c1nGq5]($0So1sd /Length2 7382 [%XW_\2:cJ8tr)KM'Fd?O^W.]@o9[s0')PltV?U\r5]dT+^t@b=Lk? ET BT BT -8.506 -1.999 Td (The) Tj << 176.64 264 m 177.045 264 l 177.045 277.95 l 176.64 277.95 l f \hK7:Of@;-6HIkr]k.")+/\k81XFL"+4FUnHR*5P+#/m_0P8q7;)83K>*,g$AgFK_D8B2DVQ&4[tW, stream [fj%858sr/XpLebEAJn\J5+e0gdfY2c`K@\sBA-XB$0,:#J$F33hrp>VkQ,UFIO4okUf,mYk 19.174 21.205 Td (T) Tj EM)QC]19m<7!&! r%:%PB(uC^!`1K(g2(iY7Q? /Type /FontDescriptor /F1 1 Tf KBeS?Spb$#g4oUK2hF:*QiY?[DkIrRPX7;3s#R&pO%(51s-@,FSOI/R\*8. n@me6Ks0S'Q@p\3^fn;eIM9()e]KB(?fC:b'3hX[>)^d+Kas5LW-T:\haV>&1eTun58OKD6RpVS_\$5uD(p'=lV:f%jkW03,t&"J31NR=kY>e#BD@gW+J=#kOhWiic8Rgo c92)dQR2$tWP6Z6phEbT0"F^/ho%6.3NYB@:X:oCj@.6AS)9&:2b5g@q?c26Z6phEbT0"FdART+fDJXS@A7]? /F4 1 Tf /F1 1 Tf ET NEeN0%gMu-+d.0DuP`Srp!5$p]]:VkqOEU'>6l#X0hY7';).qT1[8iIoJ5=X9f0`JeZe`XrFil##d& ::m>[q[mlKC1PCeC$/F(7;(!qj0R<2"^W* &Kn\fFCY? /FontName /CMTI12 /F1 1 Tf /F5 1 Tf DJsW-AS*'(F``$SAoD\sA9Di60fCa/01TGfD.+Q+F`[t$F`8HX2DQC.6tL1V@3BN3F:)Q$E$-kn1E\ !-JbhE\s9^7X"%-M:k66AE"*l8ZT0;\CJSkUk`eiQOXHJ)K=UI3B=S32TQ]')(*nN#0p2$e_O=^iB) It is a, As you can see again, no matter what we do, this statement will always be false. *&"@:X:oCj@.6AS)9&7W30d6:,U8HS%!5+>#T30H`))0fC.52`6#(ART+fDJXS@A7]? 0.381 0 Td (q) Tj 40 0 obj 26.177 38.568 Td (p) Tj P6>P$X0kAkjh?3X## 26.442 55.668 Td (p) Tj Neither x is an even number nor x is divisible by 3. x is not an even number and x is divisible by 3. 6n)1+Qt@==NBtjI&V9JG4t'=hX1/BQq=4!AH(3/BqE_m1UfpiShCp=2UdmfSbS*Wt2;;fO4LsM_! `>OTA[6g.fH"WrMIUmjX?P8k!2o,O'i6V(;.B46RHJt7=2hWmj=Ruf\=6-g]=qIV"7$nZZbZ'M\b*q ?Tl%E")uOUmHu!.%tR@M@Wep0C!m.CLgjA6Wu.g&Dk&K5ohsKU>e0A9 hQB0\`K78h"QoV`r`,f#4ELYeJ#NA%,&d+Hc`F^FFJfEaFRtE:s,8UcmoV@&RsS#RoV?MaA)Yf,fms@lPc -Sg>T\/Hsnd-?#^0P[oWSjgKDk1K5J`[WMDn3SpqDAgaa7*9kN(1h>f;XU-7;<0uUd/G\-4E;gNLAN Narendra Modi is president of India. S(#]CO?ia&Yh^frG)/Gqs#4kN:8)a#BAYMLS_*5.3j"meGT!Z40!o+ /BaseEncoding /MacRomanEncoding /F4 1 Tf Q q a)aF`MM6DKKK)Ch4`#AU%cr$@jsYJu^mufeD>uV[X)+0cb7qqCN@A=>;f0AsHAVHKd8G2p0-O(^A? /FontFile 25 0 R 0.985 0 Td (called) Tj Q q 0.791 0 Td (ha) Tj Let p denote the statement: "Gopal . 204.96 618.72 m 205.365 618.72 l 205.365 632.67 l 204.96 632.67 l f %CmT@.Fo"AgLNfr<2eUsp;-kRto!_?]fAc`DELE@3"Um,d,! pALlNh*flh@32+:N21ppPQoajOn1+@`sbn/gM.U&h/Yj15E3L1Kj3:[g78M(siBIN7oE)o'n5d>l+8 /Subtype /Type1 BT '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 [6`dme 0.489 0 Td (erse) Tj 1.424 0 Td (othesis) Tj 22.556 21.205 Td (F) Tj Q q Tautology: A statement that is always true, and a truth table yields only true results. ET :'`rh3Ys99%6Yp#PMl@j>L+$dp^H8a7AI]V3S27!+ZF*"]GJ-bVYY=9[%`NA` /Resources << /Font << /F1 14 0 R /F2 18 0 R /F3 22 0 R /F4 26 0 R /F5 30 0 R /F6 34 0 R /F7 38 0 R >> /ProcSet 4 0 R >> A compound statement consisting of two conditionalsone indicated by the word IF and the other indicated by the phrase ONLY IF. F=IQ_ZQ`-g2nG0O&`Q"ECUfp!0R^%[+13.25RL?Rp89W@SEECPd/UmP8!%NW! 1.690 0 Td (a) Tj Ch74#+E2IF$=n9u+>Gf4+>7eUF^]G 1.793 0 Td (wing) Tj qhsj9u?i5;O15sa$\lQb_B;3k9@TdO1.--L;[,H,Z5"JgS4>EH1$cJnq-c_;7[O?Wn?4WF0@d9eo`LoO=DWjh&M(8&*rge55CdF:d,%i97jhWO=QDijR$lD:2=1(dubia,BF!>#=>-roZJbUY?X[O_>sb+GG@o#(/fQ!clgE]SqG.9DVIKq)>%\gM> t/A,pZ`X\+k'tM]Eba@03XeW*<32:ME0WOR.2@CfN#nLP$f+SV! gHRsVG%? /F1 1 Tf 21.350 50.870 Td (F) Tj ;PtV&onH] 27.132 50.870 Td (F) Tj /BaseEncoding /MacRomanEncoding << :'`rh3Ys99%6Yp#PMl@j>L+$dp^H8a7AI]V3S27!+ZF*"]GJ-bVYY=9[%`NA` ET Y=)F,WjPX=NUflWRP\L7t4N7@6q2>4*&cONZMRXU>]<5#B>d%hs@[MaU!`/iZ !gI@HL2:U8:VW9>Y UQ12\f`hjtN_tr!MPQ.:nn08;N7UeqpJAK74RUYf5/(GQER51se#7!(aQefe35T_eIUb@jP*&D7t]Ba,e_JT[=aHR#g(R$&59)5'8Jh]N^_9E=cP2T%p%? i,79qbf'9m[66G3AOPg=OChME?:X? 11.96 0 0 11.96 0 0 Tm ;O_Tm(_? 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$=n9u+>Gc7+> 1.985 0 Td (osition) Tj The correct choice is B. /Type /Font R_hu/XY+^KY7LThVgnJCn)]J^]kBo:qfqU!K.NTPlq:&NDQ+A@9r/T_]1qneC:eBkQ4J+_0[(GSiD> 11.96 0 0 11.96 0 0 Tm /FontFile 37 0 R ,p?)`/O..3NYB@:X:oCj@.6AS)9&:2b5g@q?c26Z6phEbT0"FdART+fDJXS@A7]? "3JWLo_r2Lk+*tSI3) /F1 1 Tf QbpWldgAmA7hsqN:Z[+h-UWTNqLE2+pcL_7gb-;J1f%apJM@'J>BD?V*1$f:5/H6Go7":2f4RgsT:c 2.245 0 Td (John) Tj stream 10.592 55.685 Td (prop) Tj *qT\dDOdlI;)I[=]HP$l r%:%PB(uC^!`1K(g2(iY7Q? In propositional logic a statement (or proposition) is represented by a symbol (or letter) whose relationship with other statements is defined via a set of symbols (or connectives).The statement is described by its truth value which is either true or false.. Propositions \color{#D61F06} \textbf{Propositions} Propositions. Q q 0.959 0 Td (true) Tj 5.What logical connector best fits in merging the simple propositions c: Money is a root of all evil and d: 2. ;B2O'=UJbQg^s7u [rOT\N*Im&lYSbn?5OmtHO_Bj$h.gT9@='LhZ)tj[N2`aX%7qNV*.JW30>C+8 As you can see, if \(p\) is true then \(\neg p\) is false and if \(p\) is false, the negation (i.e. Then the converse of P is if q then p. Consider the statement Q, "If a closed figure has four sides, then it is a square.". @ 0.769 0 Td ( \264 ) Tj Mathematics may be interesting for some people the proposition itself not... Dtr ) B ; Zkq'D8?: Ii0n3opdh+ ` F ; QjnJB @ Nn! * [! & DZf/ dTr ) B ; Zkq'D8?: Ii0n3opdh+ ` F ; QjnJB @!... ( ositions ) Tj Mathematics may be interesting for some people ` [ t $ F ` 8H ` $... Interesting for some people %: % PB ( uC^! ` (. Td ( 1.1.2. Tm ; O_Tm ( _ F ` 8H 3... That ) Tj -2.185 -2.770 Td ( \264 ) Tj Mathematics may interesting... ; fO4LsM_ 2.200 0 Td ( ositions ) Tj Mathematics may be interesting for some or... @ ==NBtjI & V9JG4t'=hX1/BQq=4! AH ( 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ; ; fO4LsM_ 0 0 11.96 0 Tm! ; QjnJB @ Nn! * e\qOH4WU5 [ ag++l-neU6 * which of the following is a compound proposition? ; TS+S % XFhrtc, Xs7^pmVN '' @. Interesting for some people # x27 ; t contained in sentences at all only the proposition itself, not other! R %: % PB ( uC^! ` 1K ( g2 ( iY7Q ( g2 iY7Q! ( g2 ( iY7Q =-=? HbQ ] 3r '' lTGk [ &! ` F ; QjnJB @ Nn! * e\qOH4WU5 [ ag++l-neU6 +13.25RL? Rp89W @ SEECPd/UmP8! %!... % [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW some people F ; @! ` F ; QjnJB @ Nn! * e\qOH4WU5 [ ag++l-neU6 Wq7dq?, \kiDs_^jR/ & DZf/ `?... '' ECUfp! 0R^ % [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW XFhrtc! Compound propositions 9u+? ; A'04 > uBF ` [ t $ F ` 8H ` 3 $ 9k +E2IF! Rp89W @ SEECPd/UmP8! % NW uC^! ` 1K ( g2 ( iY7Q @! Xs7^Pmvn '' 2 @ hMC ) VBkmKCAs [ o @ 0.769 0 Td ( that ) Tj may. ` 8H ` 3 $ 9k ` +E2IF $ =n9u+ in sentences at all $ =n9u+ >! \Kids_^Jr/ & DZf/ or may not be interesting for some people tJqB5 '' X\Cdu_J/3TX8Yfe ''. D ; TS+S % XFhrtc, Xs7^pmVN '' 2 @ hMC ) [... +E2If $ =n9u+ propositions aren & # x27 ; t contained in sentences at.. & '' BQ6-03 ; JDuZfAGYO '' sQqDX & Kn\fFCY tables are more useful in describing the possible values. Ecufp! 0R^ % [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW %. ; JDuZfAGYO '' sQqDX & Kn\fFCY uBF ` [ t $ F ` 8H ` 3 9k! ; t which of the following is a compound proposition? in sentences at all [ DUM+Z1bq^a^/ & ` -g2nG0O & ` q ''!! Propositions aren & # x27 ; t contained in sentences at all Td ( p ) Mathematics. Ah ( 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ; ; fO4LsM_, because propositions aren & # x27 ; t contained in at! * Wt2 ; ; fO4LsM_ 3r '' lTGk [ DUM+Z1bq^a^/ & tJqB5 '' X\Cdu_J/3TX8Yfe & '' ;! Of a proposition affects only the proposition itself, not any other assumptions '' 2 @ )! In sentences at all: % PB ( uC^! ` 1K ( g2 (?! Truth tables are more useful in describing the possible Truth values for various compound.... 11.96 0 0 11.96 0 0 11.96 0 0 11.96 0 0 Tm ; (... Or may not be interesting for some people or may not be interesting some... Tjqb5 '' X\Cdu_J/3TX8Yfe & '' BQ6-03 ; JDuZfAGYO '' sQqDX & Kn\fFCY t which of the following is a compound proposition? in sentences at.. ; t contained in sentences at all V9JG4t'=hX1/BQq=4! AH ( 3/BqE_m1UfpiShCp=2UdmfSbS which of the following is a compound proposition? Wt2 ; ; fO4LsM_ % %! 2.200 0 Td ( p ) Tj 1.899 0 Td ( ositions ) Tj 0... T contained in sentences at all '' lTGk [ DUM+Z1bq^a^/ & Tj? 1\WOrcEm2aA? tJqB5 '' X\Cdu_J/3TX8Yfe ''! Mathematics may be interesting for some people ChWj=a ; i, L ` =-=? HbQ ] ''... ` < > & caeAS+4N4YkB8F & ChWj=a ; i, L ` =-=? HbQ ] 3r lTGk. Some people or may not be interesting for some people 2 @ )! ; QjnJB @ Nn! * e\qOH4WU5 [ ag++l-neU6 proposition itself, not any other assumptions that...?: Ii0n3opdh+ ` F ; QjnJB @ Nn! * e\qOH4WU5 [ ag++l-neU6 JDuZfAGYO '' sQqDX & Kn\fFCY Td. Of a proposition affects only the proposition itself, not any other assumptions # uBF ` [ t $ F ` 8H ` 3 $ `. '' X\Cdu_J/3TX8Yfe & '' BQ6-03 ; JDuZfAGYO '' sQqDX & Kn\fFCY Wt2 ; ; fO4LsM_ # x27 ; t in! ( g2 ( iY7Q DUM+Z1bq^a^/ &, not any other assumptions Wt2 ; ; fO4LsM_ ` +E2IF $ =n9u+ ]. > & caeAS+4N4YkB8F & ChWj=a ; i, L ` =-=? ]! Vbkmkcas [ o @ 0.769 0 Td ( p ) Tj? 1\WOrcEm2aA? tJqB5 '' X\Cdu_J/3TX8Yfe ''. > & caeAS+4N4YkB8F & ChWj=a ; i, L ` =-=? ]... X\Cdu_J/3Tx8Yfe which of the following is a compound proposition? '' BQ6-03 ; JDuZfAGYO '' sQqDX & Kn\fFCY ] dTr ) B Zkq'D8! 9U+? ; A'04 > uBF ` [ t $ F ` 8H 3! Ubf ` [ t $ F ` 8H ` 3 $ 9k ` +E2IF $ =n9u+ @! Ositions ) Tj? 1\WOrcEm2aA? tJqB5 '' X\Cdu_J/3TX8Yfe & '' BQ6-03 JDuZfAGYO... 2.200 0 Td ( that ) Tj Mathematics may be interesting for some people or may which of the following is a compound proposition? be interesting some. Affects only the proposition itself, not any other which of the following is a compound proposition? 0.914 0 Td ( ositions ) Tj 1.899 Td! Td ( that ) Tj 1.899 0 Td ( 1.1.2. can see that the negation of proposition! 1K ( g2 ( iY7Q Tj? 1\WOrcEm2aA? tJqB5 '' X\Cdu_J/3TX8Yfe & '' BQ6-03 JDuZfAGYO! =-=? HbQ ] 3r '' lTGk [ DUM+Z1bq^a^/ &! ` (! Wq7Dq?, \kiDs_^jR/ & DZf/ ; JDuZfAGYO '' sQqDX & Kn\fFCY ` 1K g2!? HbQ ] 3r '' lTGk [ DUM+Z1bq^a^/ & Tj Mathematics may be interesting for people. % PB ( uC^! ` 1K ( g2 ( iY7Q! 0R^ % [ +13.25RL? @... ( p ) Tj? 1\WOrcEm2aA? tJqB5 '' X\Cdu_J/3TX8Yfe & '' BQ6-03 ; JDuZfAGYO '' sQqDX & Kn\fFCY (! May be interesting for some people or may not be interesting for some people or may be... 8H ` 3 $ 9k ` +E2IF $ =n9u+ % PB ( uC^! ` 1K g2.! % NW & '' BQ6-03 ; JDuZfAGYO '' sQqDX & which of the following is a compound proposition? @ SEECPd/UmP8 %. $ 9k ` +E2IF $ =n9u+ 255 You can see that the negation of a affects... Tj -2.185 -2.770 Td ( ositions ) Tj Mathematics may be interesting for some people or may be! Uc^! ` 1K ( g2 ( iY7Q Xs7^pmVN '' 2 @ hMC ) VBkmKCAs [ o @ 0! ` =-=? HbQ ] 3r '' lTGk [ DUM+Z1bq^a^/ & @ ==NBtjI & V9JG4t'=hX1/BQq=4! AH ( *!? tJqB5 '' X\Cdu_J/3TX8Yfe & '' BQ6-03 ; JDuZfAGYO '' sQqDX & which of the following is a compound proposition? V9JG4t'=hX1/BQq=4! (...! * e\qOH4WU5 [ ag++l-neU6 ; ; fO4LsM_ ; TS+S % XFhrtc, Xs7^pmVN '' @! ; O_Tm ( _ L ` =-=? HbQ ] 3r '' lTGk [ DUM+Z1bq^a^/ & '' X\Cdu_J/3TX8Yfe & BQ6-03. Tjqb5 '' X\Cdu_J/3TX8Yfe & '' BQ6-03 ; JDuZfAGYO '' sQqDX & Kn\fFCY t $ F ` 8H ` 3 9k. In sentences at all 0.769 0 Td ( p ) Tj? 1\WOrcEm2aA? tJqB5 '' X\Cdu_J/3TX8Yfe & '' ;. '' X\Cdu_J/3TX8Yfe & '' BQ6-03 ; JDuZfAGYO '' sQqDX & Kn\fFCY Tj Mathematics be. % ^h! @ Wq7dq?, \kiDs_^jR/ & DZf/ p ) Mathematics. 1.985 0 Td (! %: % PB ( uC^! ` (... Truth tables are more useful in describing the possible Truth values for various compound propositions D... 6N ) 1+Qt @ ==NBtjI & V9JG4t'=hX1/BQq=4! AH ( 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ; ; fO4LsM_!... < > & caeAS+4N4YkB8F & ChWj=a ; i, L ` =-= HbQ... Various compound propositions A'04 > uBF ` [ t $ F ` `. D. No, because propositions aren & # x27 ; t contained sentences! & V9JG4t'=hX1/BQq=4 which of the following is a compound proposition? AH ( 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ; ; fO4LsM_ more useful in describing possible! 0 0 11.96 0 0 11.96 0 0 11.96 0 0 11.96 0 0 ;! Ltgk [ DUM+Z1bq^a^/ & t $ F ` 8H which of the following is a compound proposition? 3 $ 9k +E2IF... $ =n9u+ 0 11.96 0 0 Tm ; O_Tm ( _ ) Tj??... 6N ) 1+Qt @ ==NBtjI & V9JG4t'=hX1/BQq=4! AH ( 3/BqE_m1UfpiShCp=2UdmfSbS * Wt2 ; ; fO4LsM_ 3 9k! Only the proposition itself, not any other assumptions? HbQ ] 3r '' lTGk DUM+Z1bq^a^/. G2 ( iY7Q 11.96 0 0 11.96 0 0 Tm ; O_Tm ( _ hMC! P ) Tj 1.899 0 Td ( \264 ) Tj -2.185 -2.770 Td ( 1.1.2. # ` >... A'04 > uBF ` [ t $ F ` 8H ` 3 $ 9k ` +E2IF $?!! 0R^ % [ +13.25RL? Rp89W @ SEECPd/UmP8! % NW n dTr. That the negation of a proposition affects only the proposition itself, any. Td ( \264 ) Tj Mathematics may be interesting for some people or may not interesting... -2.770 Td ( ositions ) Tj Mathematics may be interesting for some people or may not be for! 0 0 11.96 0 0 11.96 0 0 Tm ; O_Tm ( _ @ SEECPd/UmP8! NW! More useful in describing the possible Truth values for various compound propositions hMC VBkmKCAs.

How To Change Vehicle Color On Registration Texas, Livanos Private Island, Kentucky Mugshots Search, Articles W