ࡱ> EGDy -bjbjEE 44'' %$$ggggg{{{8T${+t++"MMM(((:+<+<+<+<+<+<+$_-0`+Eg(((((`+ggMM+(gMgM:+(:+&h'M9_Xd{p'&++0+'|0 0 '0g'(((((((`+`+(((+((((0((((((((($ -: SYMBOLIC LOGIC TRANSLATING INTO SENTENTIAL LOGIC Translations from natural languages into logical formulas have certain properties. They are concerned only with truth values They miss out on subtleties of communication (for example, we translate but, although, and despite the fact that as and). Atomic Claims: Represent each simple claim with a capital letter that corresponds to the sentence (to make it easier to remember). For example, represent the sentence Kara got her hair cut with the letter C. Sentence Connectives: Represent (truth functional) sentence connectives as follows: ~ (NOT), & (AND), V (OR) and ( (IF/THEN, IMPLIES) and  (IF AND ONLY IF). In conjunctions, the left conjunct goes to the left of the connective and the right conjunct to the right. Conjunction symbols must have a formula on each side. Example: English: Kara got her hair dyed and cut. Sentential Logic: D & C In disjunctions, the left disjunct goes to the left of the connective and the right disjunct to the right. Conjunction symbols must have a formula on each side. Example: English: Kara got her hair either dyed or cut. Sentential Logic: D V C Parentheses can be used to control the order of processing. For example, if you wanted to translate the sentence If you either attend enough classes or go to a presentation you will get a good attendance grade, then you would use parentheses to show that the antecedent is made up of two disjuncts enclosed in parentheses, as follows: (A V P) ( G In negations the NOT symbol goes to the left of the formula. Example: English: Kara didnt get her hair dyed. Sentential Logic: ~D If you want the negation to affect a compound formula (and not just the atomic sentence immediately to its right) you need parentheses. Example: English: Its not true that Kara got her hair dyed and cut. Sentential Logic: ~(D & C) this means not both In conditionals, the antecedent is connected to the consequent with the ( symbol, with the antecedent to the left of it and the consequent to its right. Example: English: If Kara got her hair dyed then she got cut. Sentential Logic: D ( C NOTE: You must get the antecedent and consequent in the right order around the connective since it says something different to have it the other way. TRANSLATING FROM ENGLISH TO SENTENTIAL LOGIC Identify and circle each sentence connective in the English sentence (and, or, if/then, not, if and only if). Identify and circle each atomic sentence (or shortest complete sentence) in every sentence and choose a capital letter to represent it (one that makes sense is best). Create a dictionary showing what sentence corresponds to each capital letter. Write each sentence connective in its location (and -- &, or V, if/then (, not -- ~, if and only if -- , leaving blank spaces for parts). Determine where to put each capital letter corresponding to the different atomic sentences (for a conditional it s important to have the condition or antecedent before the conditional symbol and the res 0123 0 1 3 4 ۶綾xgxVxgxgxgxgxHh!CJOJQJ^JaJ hfhCJOJQJ^JaJ h]hCJOJQJ^JaJhCJOJQJ^JaJ h(|hCJOJQJ^JaJhTCJOJQJ^JaJ h(|5>*CJOJQJ^JaJ&h(|h]5>*CJOJQJ^JaJ h]5>*CJOJQJ^JaJ&h(|h(|5>*CJOJQJ^JaJ hT5>*CJOJQJ^JaJ1233 4 N P J U  < G w gdTdhgdTdhgd!gd! & Fdhgdgd & Fgddhgdgd(|4 ; A B D    4 8 : < ɻp_QhO0CJOJQJ^JaJ hahaCJOJQJ^JaJha5CJOJQJ^JaJh!5CJOJQJ^JaJhpCJOJQJ^JaJh!CJOJQJ^JaJ hh!CJOJQJ^JaJhaCJOJQJ^JaJ#hxhO5CJOJQJ^JaJ&hh!5>*CJOJQJ^JaJ h!5>*CJOJQJ^JaJ   H J V n J Q U \  : ; < C G N c j o ӱӝӋӋӱwiWiIihz*CJOJQJ^JaJhTCJOJQJ^JaJ&hThT5>*CJOJQJ^JaJ#h!h!>*CJOJQJ^JaJ&hTh!5>*CJOJQJ^JaJ h!5>*CJOJQJ^JaJ hh!CJOJQJ^JaJh!CJOJQJ^JaJhO0CJOJQJ^JaJ jhO0CJOJQJ^JaJo q w def./6ijuaS?&hTh S5>*CJOJQJ^JaJhdCJOJQJ^JaJ&h!h!5>*CJOJQJ^JaJ jhO0CJOJQJ^JaJhO0CJOJQJ^JaJh SCJOJQJ^JaJ hTh SCJOJQJ^JaJ h S5>*CJOJQJ^JaJh!CJOJQJ^JaJ#h!hT>*CJOJQJ^JaJhTCJOJQJ^JaJh CJOJQJ^JaJ /:cyzK +az{)dh$d%d&d'dNOPQgd Sdhgd!gdTgd SdhgdTdhgd Sgd!6:Acsz K[f '+Ķo^J&hThT5>*CJOJQJ^JaJ jhO0CJOJQJ^JaJ&h!h!5>*CJOJQJ^JaJ h S5>*CJOJQJ^JaJh1CJOJQJ^JaJ&hTh S5>*CJOJQJ^JaJhTCJOJQJ^JaJh!CJOJQJ^JaJhdCJOJQJ^JaJ#h!h S>*CJOJQJ^JaJh SCJOJQJ^JaJ+25\aqvwz{AZmn߯|hWCW5Wh!CJOJQJ^JaJ&hh(|5>*CJOJQJ^JaJ h(|h(|CJOJQJ^JaJ&h!h!5>*CJOJQJ^JaJ h5>*CJOJQJ^JaJ h Sh SCJOJQJ^JaJ h S5>*CJOJQJ^JaJ hT5>*CJOJQJ^JaJ jhO0CJOJQJ^JaJhj}CJOJQJ^JaJhTCJOJQJ^JaJ#h!hT>*CJOJQJ^JaJAWXjlJ,K,Y-Z-c-------dhgd(| & F #dh^#`gd!gd & F #dh^#`gd(|dhgd! WXakl´򣏣}l}[ h1hCJOJQJ^JaJ hHhCJOJQJ^JaJ#hO0h5CJOJQJ^JaJ&hh!5>*CJOJQJ^JaJ h(|h!CJOJQJ^JaJh!CJOJQJ^JaJ h(|h1CJOJQJ^JaJh(|CJOJQJ^JaJ h(|h(|CJOJQJ^JaJhCJOJQJ^JaJ "&4Nbdhl,,,,,,,˹˹˗ˆuuauu_uauuN hO0hO0CJOJQJ^JaJU&hO0h(|5>*CJOJQJ^JaJ hO0h(|CJOJQJ^JaJ hO0hC+[CJOJQJ^JaJ h(|h(|CJOJQJ^JaJ hO0hCJOJQJ^JaJ#hO0h5CJOJQJ^JaJhCJOJQJ^JaJ h1hCJOJQJ^JaJ) jhO0h5CJOJQJ^JaJult or consequent after it). Write the letters in the appropriate spots. If there is more than one sentence connective, identify the main connective of the English sentence (that affects the biggest pieces). Add parentheses to the formula so that its main connective corresponds to the main connective of the English version of the sentence. Example: If you attend the study skills workshop and bring in the handout you will get attendance credit in the class.     PAGE  PAGE 3 ,#,J,z,,,,,,,,,,,,,,, --!-0-Y-Z-a---Ϳ͆ͿrrarSh(|CJOJQJ^JaJ h(|h"X#CJOJQJ^JaJ&h(|h(|5>*CJOJQJ^JaJ&hh(|5>*CJOJQJ^JaJ&h h S5>*CJOJQJ^JaJ h(|h SCJOJQJ^JaJh SCJOJQJ^JaJ h(|h(|CJOJQJ^JaJ hO0h(|CJOJQJ^JaJ hO0hCJOJQJ^JaJ------------------------h0JmHnHuh S h S0Jjh S0JUhDjhDU h(|h1CJOJQJ^JaJ-------------dhgd(| &`#$gdT 21h:p]/ =!"#$% ^ 2 0@P`p2( 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p8XV~_HmH nH sH tH @`@ (|NormalCJ_HaJmH sH tH DA`D Default Paragraph FontRiR  Table Normal4 l4a (k (No List 4 @4 TFooter  !.)@. T Page Number@@  List Paragraph ^PK![Content_Types].xmlj0Eжr(΢Iw},-j4 wP-t#bΙ{UTU^hd}㨫)*1P' ^W0)T9<l#$yi};~@(Hu* Dנz/0ǰ $ X3aZ,D0j~3߶b~i>3\`?/[G\!-Rk.sԻ..a濭?PK!֧6 _rels/.relsj0 }Q%v/C/}(h"O = C?hv=Ʌ%[xp{۵_Pѣ<1H0ORBdJE4b$q_6LR7`0̞O,En7Lib/SeеPK!kytheme/theme/themeManager.xml M @}w7c(EbˮCAǠҟ7՛K Y, e.|,H,lxɴIsQ}#Ր ֵ+!,^$j=GW)E+& 8PK!Ptheme/theme/theme1.xmlYOo6w toc'vuر-MniP@I}úama[إ4:lЯGRX^6؊>$ !)O^rC$y@/yH*񄴽)޵߻UDb`}"qۋJחX^)I`nEp)liV[]1M<OP6r=zgbIguSebORD۫qu gZo~ٺlAplxpT0+[}`jzAV2Fi@qv֬5\|ʜ̭NleXdsjcs7f W+Ն7`g ȘJj|h(KD- dXiJ؇(x$( :;˹! I_TS 1?E??ZBΪmU/?~xY'y5g&΋/ɋ>GMGeD3Vq%'#q$8K)fw9:ĵ x}rxwr:\TZaG*y8IjbRc|XŻǿI u3KGnD1NIBs RuK>V.EL+M2#'fi ~V vl{u8zH *:(W☕ ~JTe\O*tHGHY}KNP*ݾ˦TѼ9/#A7qZ$*c?qUnwN%Oi4 =3ڗP 1Pm \\9Mؓ2aD];Yt\[x]}Wr|]g- eW )6-rCSj id DЇAΜIqbJ#x꺃 6k#ASh&ʌt(Q%p%m&]caSl=X\P1Mh9MVdDAaVB[݈fJíP|8 քAV^f Hn- "d>znNJ ة>b&2vKyϼD:,AGm\nziÙ.uχYC6OMf3or$5NHT[XF64T,ќM0E)`#5XY`פ;%1U٥m;R>QD DcpU'&LE/pm%]8firS4d 7y\`JnίI R3U~7+׸#m qBiDi*L69mY&iHE=(K&N!V.KeLDĕ{D vEꦚdeNƟe(MN9ߜR6&3(a/DUz<{ˊYȳV)9Z[4^n5!J?Q3eBoCM m<.vpIYfZY_p[=al-Y}Nc͙ŋ4vfavl'SA8|*u{-ߟ0%M07%<ҍPK! ѐ'theme/theme/_rels/themeManager.xml.relsM 0wooӺ&݈Э5 6?$Q ,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-![Content_Types].xmlPK-!֧6 +_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!Ptheme/theme/theme1.xmlPK-! ѐ' theme/theme/_rels/themeManager.xml.relsPK] 4 $$$'4 o 6+,--  --   '!!8@0(  B S  ?  ^` 331233CDx{fvw  V W X X    ' 1     z   1233CDx{fvw  V W X X    ' 1     {+ Jh0 Jc0 JJHfSiQ8^`.8 ^`hH.8 pLp^p`LhH.8 @ @ ^@ `hH.8 ^`hH.8 L^`LhH.8 ^`hH.8 ^`hH.8 PLP^P`LhH.8^`.8 ^`hH.8 pLp^p`LhH.8 @ @ ^@ `hH.8 ^`hH.8 L^`LhH.8 ^`hH.8 ^`hH.8 PLP^P`LhH.8^`.8 ^`hH.8 pLp^p`LhH.8 @ @ ^@ `hH.8 ^`hH.8 L^`LhH.8 ^`hH.8 ^`hH.8 PLP^P`LhH.h^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHc0{+h0SiJ                           8fwhm rg1 % W9 Iy@545Td$#GiaH?=!%Y O0y@OPAh '#A#"X#C$@%&@(h|(l-!/0M2"353d 4|40:;C=|?`E@hBmCM%EwEF#FJHa-J*M9MO9(Q SyU#WM8W@MXCYH+Z%zZC+[]3]^I^xanBasa +b0Ccd+e[f+_f$gRgmij VjmjGkRk]knp>rBrIsttpv\xz'Q.bK{5DNcad 96B] '7  ))B0l_\RV[p X4lFR*V;sz5GVs xC )(|bA3pt:17j}nw}h!ci*"H*]+* ,j$+Q @  8N  @ @ @X@UnknownG* Times New Roman5Symbol3. * Arial?= * Courier New;WingdingsA BCambria Math"1h`FC  !4d 2QKP ?(|2!xx*TRANSLATING SENTENCES INTO SENTENTIAL FORMpdn26pdn26      Oh+'0 ,8 X d p |,TRANSLATING SENTENCES INTO SENTENTIAL FORMpdn26 Normal.dotmpdn265Microsoft Office Word@xA@K]"@ab@LAXd ՜.+,0 hp  CSUS  +TRANSLATING SENTENCES INTO SENTENTIAL FORM Title  !"#$%&'()*+,-./012356789:;=>?@ABCFRoot Entry FT_XdH1Table0WordDocument44SummaryInformation(4DocumentSummaryInformation8<CompObjy  F'Microsoft Office Word 97-2003 Document MSWordDocWord.Document.89q