HD} “Uy tptp sq) = PANY LHS Jaws 1 (pq) Conditional ‘T (tev 4) Domorgan!s AMP Any Dotwble negediop PANY beP TWeenadv CPA44) SP Lars LHS Ceaad V CPATY) pigdetbective PAU 199 eo mploment PAT srclantity P Ponce proved iv) (eva) A CPVIM =p tpvy) ACPV 7p) Ofsyibustive PV CAA TP) eamplamence yas PvE eae vale 9) = (ra 74) V (1PAV) Cee V) Bicondittonal a travnnr? a) conditioner a(apyvA cape) ) Hemosigan H\hemorgon 4) vt (It p)) 4 (tty Vy (ren “1P) Double negation ap)A14_—_ Jima yaa) VLAP (rs (TATIP) powcrnuetatt ue pat) vet ( (1p ne PAV) Hone proved anlotiso2y . gine each ag te pouowtng an dn symbolic form, ano good wu good aya men p)NoO me come NEN ons au hot good. good dy Some RP Solm bt mix)i x ds a mon. & Qcm) ‘oe is good men a) Fox alas & aT a fs a goad a Is gooe yon Emin & oJ b) Foot ab a O) ig oo ds a men dahon oO Ss not good ‘ jgapmed? 4 acs) 5 Some Orot edt OC > de. bs <) fom some a ,guch gheet fs ob men: then Se fe oO Good + Ja Timex auex) ] Aipor bsome = SUE} Pe oe Say net goed + a Jd 4 a CUtx) Kae) )* Bor ip rr ee Vontabte 3 Rand wat Ww “the vaniatite cls gat cto bmuind ety tt 4 © aioel Comstimed with — cath aurfivensal bot weattens ice Foam tclal dnmedlerteta Scope: my Formula nl QYollow vne quantigion s Vartalye : pay diac ath te Det eonsumed with one querretigten AS Catlral groo Yat Eg * \) oo [pte yd) x3 bound tne GaPiony) Plx.y) 2 Scope (+ KOI ) poe Vartabte 5 y , 2) Ya lee) A atx) a bound Lyn Hoe [T PDA atar] Scope 3 PCa) A Ata) spre Vouluie > No 3) tx) [peo UBy) aloe, J a2? bound &r toc) —__ yo pound 4n(gy) tery)scopt * pioe) (ay)& (x99) of ys QL iho wm > ote pscas ent ina pros Vank clxte ; ° angere nce g athab dy 9 predicate Ce : Dees: eurtvercot spactgtcasion J AEH! 7 Aly) gy Rute ES * Teaftstensial ppc vee) Ate) 2 ACY) mun OG: Tuntversat GopntobzorDns Aty) 5) 2) Ate) h) Rute BG: ocfstential Gunnell Aw)> FAC) , 3) action J ote | + adhe funy aj ingouence fon tho praclicete uo used gollowing gostmutar Pyevalanes., PAWeDtODY « pute Ty Rive aleulus fn! one is ue e 2 . P, Implteatiion , Rule “Tp dinalirect mated $B er ee the find yre solution , fvoTe 2 ¢ do wiminate 44 Seton uw e wan mule 3 ae A c twe the shecigucicon Cus NOTES! ES) fo pois tht corrert quansigiom me can inte < : dnek Sule ef genmols zatron TYG, es] a. eee eee ee: | fy athe Vaticlity ap dhe yoltow ing AAQumarcs map atm his ana ver clangenous anima. "eThonre Q 1 ddions ' 2,9 au ufons adhe an danguious animal Sr TC 1 DE RK (of Leo) :a fe a tion. , b Dee) \ ow Fas a, dangerous animal oy x [Ltd Dexd} , oc, Face.) s = oc (2 (00?) Ss Poemise 2 VOLE Lted- Disa) , Pollen) Ponculsion S3a (Dees) EP : oe ] Raseson () voc cae Bo - 2) Luo Oty) Eke i seaternent Ruites | Rosen n Me ae Ris P 21 by) 2 pty). Pato VE iy i a Sto) Th (x) J Rute P Hn) sty) P Rehirp « 5) Sty ) Pops Rudo Thy (eq jp) =4 b) Foc Pid Moods bonss Run EG “dhe condition fs oth, ———————— Tewan ntegert dis .atvistons wy 10 dhan eit Ga ay gnisiote ay 2° St db divisibta by Gs Thoregoog the Vntegqo ne ¢ Alto AiViBibia by %. 88 can dntaqor ds adivisiol Log 9 athe aiisite by 1° co Soin: ‘ . Dole) $ ow cds divislo by Jo. Dato: x As divisible by 2 Detar © ds visible by 8. Premises % spor [Ob (2) Dated], Yo Too td) 9 dsl). concleision ¢ ye [Dota)— Dated) vex Symbolic pom 3 Hx (Oe (x) » DIA), Moe (Da (ar) 9 Ds tx) P-¥2 (Diet PDs te) Step ‘ Statement Rurs | Rearon 1) sea (Diotsd > Da) Rute Pp. 2) Dio ly) 3 Datyd Rua Os. 3) MY xls (a) Ds (er)) Rubs P 4) De (yy DDS ty) Rule OS @ Dost. Dsly) ("gmtnettenl b) “ee (Bip (2)—9'Da (ed) one i tee ‘QR vie tnshy ') $Me that prempyone student fh thir class knows hew — to ‘wate proprame Th Java , AX gueryone who knows how to Lurete Program fn Tava can got a high paying Job. Tnipubs fhe concutston Some ove th Las Gays got a ATghk paying p06 . Soln: Atsc) 1X fs In the elcid Bit) : 90 lenouss Tava poropamming , ctx) : oe can got a high paying Job. . pstemises * Fux) (Ata) A Bex)) ya [Bods ctx) 7 Coneeteion zoe TA (BIA ¢ tee) J: ‘Aip Poomise, Rute /Reason { Fu (Ata) A Bla) ) » Ruto P 2. AWAB LY) Rue ES Sa ep Aly) Rupr) Stmpulbiccerion Ae B (yo TNF afm pl Cassy . B- yoeltt90'7) Rul po aay ee eet ol) Rule US. Rue T4358.) 4 cw ch Pa Yoq ereConfunctlon Rite T A M14) a) sex) CAD A COX) 5 Reto Fa a) Aty) A ecy) Q) Shee dhat § Bax ( peda o (x)= [ (dx) pes)) A a (aerate) Poemise : gar a x pOa ace)) conclusive’ (eax) Pear) A CHre Ca (20) ginp Poromisor Rute » Doc LPeacd a ate) Rule P 2) pey) A @CY) Puts 3) Pty) Pure 71) Stop x) pty) gute TC) 5) Ply) A cy) conjunction method. \foa ail oc appuied gndirect cx) PCO VF & aca) aAP (x) (ptx) V @ (xe) = Aysume “> concasalon 1 [ex peo) V oo acs) J gon Poconiises ule en ) Ate pen V Ix Otc) Qure AP a) 1 (vrpce)) A Th ata) Ruse T Cr) Denorgan 3) Danpom) A A oon tx) Paue T negetion‘gill (anaes caine. Ce ER NOE Er 4) Dox pen) Rue T (sim pecpiins 5) tro Taw) a " &) “+ Pty) Quire ES 4) t aty) Qu US ?) “IPYDA racy) — Confer tuan 9? 4 (Pcy) v tery) Ye megans ) Ve cre Vac) Bue P nn) pty) v aty) Runes 1) F Roe 1 (4,19) ea conjuction which 1S ¢onsa?dfaton . 1 SET THEORY : ~ Sot 1 a. epttection . held dad obpet and Its deneted by. ane kiss taal, at) Rpnnentasion of act ; set builder efoom xe Roasts fost zVenn diagram. © Set Opoiatons © yup ctaiees ov e288 ee- poe ANA OE ne ee e ee ao® i. 4 gx /saea § Te YAS peas fa /x gVant wo ¥ A} A~B © ALS farmer § agay Symmetttc genre (a @w, Aas, Ate) ADB Carsyuts -A) Jauy 2 CSet Sarnuitipy Dtaennrty awry AVA AS AnUsA . a) porminant tee AUuTD © UW) ands - §)daarpoteree (cud 9 ADA ® AJ ANASA , &) Comptement, | two AVAL SU ) Andled B)Deminant = taro ATA &) commutative din “Aug = BUA 4) AesoStatiive larva AU Cbue) (Avs) be 8) Absorption taro 2 AUCUB) = A 9 Angndte A 4) Demorgan's uno 2 AUB = AnBs Anbe A UB DPxove tat by uslng set bubtelers pornxction AnB=B0A LHS s- ( anpe {2 /sc e (ANGIE > {x Joos A and 2 € BP = fm/X 8B and @ SAS e fr /BnAsZ « RHS eeCO ——————— hh Det: Ane = Avs 4S: 4 ANB = f cele g cane} @ falrga cord BF = tale ex co) eebs = fa/set VBP = fa/se AvBt = AuB = Rus 3) p.tilA-c) n(e-Bv= > craggy A,B, C-sets vediey graphy Quse membership dterbte Show “that Pe enc ANgoC)= tang)u CAnc) -930 & ee ~~~ —-99o.0°9 > Buc AncCeuc) (ans) cane) 2 eo 0 ° ! o ° ! © a 2 { a 8 ° 0 ° } « { t ° : t t \ o | | pS = RNS Hence proved o- 8-9-2 3, tang) utane) = -—700006yea care) OC cn + dh anayticattyy Ay te went yom vee: al! jus Jn (eb) * (mo and ove cand) area fovsoe CA and xq B43 s cb and x 4 BY efm/a eA and le © {aloo EA Nh and og BY tx lo eg ands 2 BF © ‘ papxe FrBS igieedh: PFE yenn dfagram: 6 Ff . (Are) e ae aa (A-e) nce-B)= 4 Hence proved . Qt A,BiC be athe acts ST AUBnc) = COR)NA using aet Sdentitio : Spins LHS, = AuCBnc) » © Bn (8nG) (de Horgan’s ) eAn (Bue) u = (BUCINA Ccommustontive ) « CeuB)NA " Ins eRHS. Hene Moved +AN) us ims loqival | Dust Membewnin rable, Venn diagrams |g “PPV0A op Mant ancauc) + (AN B)U Chine) Agtn, Venn d hag» 1AM , f / Wy Uy) \ aby ) 4 “+ PNCBUC) ¢ tans)u tanec) fHS > RHS Hence paoved.pnts! PN! PROHUCT ig: ee A & B anc any Jwo cdot cthe ecurtes Zin q depfnod a3 2h aut Of Ordered oe Ag 8 fs prodcict (a)b) evhew a €&A and b eb pat q Hee OTM AXS< Pra) fa eA and beng en? Ae £1) 235 gett 2g Ay8 eft) Cha) (a y1)p02 12) 081081205 DAgBic oe 3 Ant Ax Canc) = CAXB) n CAXC) 1s , pxctend= {tarB)/aea g be enc = Xasb) /ashand beB % bec) = Ttarb)/aer and beBand ath s pecs Coxe eptas [a2 (A x8) andtee AX = 7 (avs) nae) 3 a)gind He uct AGB, Sp AB = F1,3,78, j > pers $2rb, 83 ANB = T4193 4 / i) AcBe WUi2AS > Bowe GAS, AvuBe $1,2) 4151123 1) th) zh) i) : ame Aes ADS SORE Mp Spd. We UF Br fark, beyBee Be) (B-"), lez) ASP reap yeas B= $5,119, 93 Relations T= {tare /aen bes 3 1 dratn ge R a Wb EB b) | 8 wand ae = f (bla Ty pss: Properties 9 Rebalon TF Ris elation” 4h 1 Regueatve % lajay eR Hae ‘N) Symmeir® tard) eR 2 tha) eR Tian symmed 2p tare) ER (badFR wes ash piansiasive “Cai CR whenever carb) and (br 6) SE TH R NS Sepntve go AKA s4aen V) Tnoepentve *