Sets: at Ait menavnem Set Ary wo0ell elafined — callection af objects = set af mete — mumbens, get of boy girl, sel of courses dh &Tethy ete Forms to represent Sets A. Tabular cfawa 4 i A sek can Ge clafineet bY visiting its ¥ numbers a sepanatect and enclosed in a Groce, j ven AY. eae aedt iat} i Be LA ey nore BW ES. 2. Set Builder fam: t the ik Ao eet con. Ge cased by stenbhy chamctertiag trae its: element mart soxtisify ee Ke CL niu © sek of all Seve? integus b. Ke Comm | set of all “ve integers } if Types of Sets! > NULL sets A set thet doegnt — conteting any element ts called a = NULL get. Denote by g ar %e{rfr€ bene ap =o ye duly en, varyA set is said te te Vs . ip tke contains every - set uncer Alscerssis fon dE ie ad © Grows 0 tinwenad set of etisclocer yD AE human ya the ant ® ae Oy D Set Jneusion & Sets: het Xe Y Be too sets Ff every leno it a, Cag ey RT EC i haa suset of (Yank is ote OF me Cy, a X= Labed 1 YH Laos , Lareyr, wets wo yk se g 4 BER VEZ % wwe se a in Jobe? . . EX every set is a subset t itself t. a An empty set aoa subet of eveny Se W Proper Set! . : mn x and Y be pera ce se Cees Let mn sult oY ro} see gp oe F x ‘ kam obeets ONE dlemonk My’ WE Ons age om, Be denoted ty KEY er xe Luasj 97k Ves KC YS) Equal fe lrs Two seks KY ow said tb %4 equol) 1 Kb suse yf GY cond Cc a % te equel ob Y- Co eeu eG a xey) EM ope Read eur htety BEDS 6) Etalke Sols J Mog elements in @ cee finite ae ecimable agen Uth set br fintle . xe La, cr ho gi fit tf eel tpt, ee deo a number af elements aap sel ‘dmet oe pot counts then K ws said © infinite- a D Power set: The collection gf subsels fa Set x ois called a power wee of Kank th dlenbtest PCa) oe P| oF Re Luzy poo dih, dey, Curse fey 9 Aisjownt Sets Tuy Seb REY ae sald H- be digant Fy Fe Aements Bebveen, +H gets, ie, TO element ¢eo and — nob element — of tr te a BD Kelas ye Lu“ay & Operation — af Sets> nion of see Srrterce ction, ¥ Ses y the union gf HO sets ) The jntenection of ats two is degiud an whe EG AY ay cal Bh SA alk clenenty tha Oe contaning alt the clement menbes of See SG aha belong te both oc Garg aodk ee demetel onal. SEY densted 6 | Ok ky Ang. 3) Properttes : 3 Properties = AUB > A& Aaa tA AUd = & Aagd=@ Aus =H Aape® AuvAR ey AOA =o pm #cG@od, ort & cee) nay ca ooh (Anges Ave = ROA Ang =K06 Av@ud = @vMoc Ancan) = Cang)ac: ca murnelly, Disysint — Seke* A collects of sets called clajoints x eveny par geke 8 Ya HE eailection i dagqaiaes4 Difference of to sets The — cliffrenco of any —-tuso Sekt A&G is the same oF elements that belongs me A far mot RB SE chemoted OY A—B HAT, =e Luter 1G= LU eye a-B > Lys « Complimeat, S a sets onivercal [eek Gov ang. Let sul Be othe Be Sy Ra led eae ae GE A and i is denoted Gy Aca A! J * Symmetric Difference tse Sete fez A end Q be any ese Sets. The symme frre difence af A ack QB Be. set comsiticg gf all a elements treat helo A or B) Sue met WH SHH AEG SE denoted Gy AOBIAWG ASB LAlREA ad agok BLx[ eee ant xead j s @-8) UCB-A) Papi Bee Ag Ge two Sete tan | A tA ~ Ha Acd c& A+ G zara Aa g's aue)- Cana) eg ack tuy ,aedsry Ant ans Avo> Gaaece-A = lau why ea ; Sve {Ge + Cartesian Product Cantesion product of A&B) dencted ry AKG fe the sek those | memeem ama alt possifla | avdered gates Carb) where 0 se member gf A ork bet arbor a coh Te PF LES ond Cred peslitte ig {Cu wed) Curwhite) , Crsred), Co nohite yy. “Tote 4 3) Set Kdentes- identity ANU=A AUG TA Avg =U ace + & AVA © = AAA 4a C= 4 AbR TBOA Ran. SO Ay Cave) = G98) SC aacancy = @adgac Au Caac) = Coa) mavuc) Aacave) = eAQocancd AAG = ALD xoa 8 ROS KUCAND) = A Aacavs) FA Nome gdentiby las amination la Lawss Sclempotent comnplumensetion fo carnmatce ve laws pyodakive Wor Duribatve GOs ade Morgans loss or Absovptton camp erene (eure* Principles gf dnelusing and -€nelusion + tasks ame done ak am, “the ang wayt ig cane dome, Ey Aihen the EONS ; Same — Bff_ ime, sto count woltich anyone gf the tasks pum bt of woyt and then af doing — each of odd the the two ES sueract th nog v Gath — doing, the tasky. THI technique \ wou _ called prineigl af jactuston — & exclusion. | Aincipal? gcc pa B rhe any Bo finite Sets the a the anton Of the HHO the no-of elements sum of the numbers — of elem ye thet A and Go is sth. ia the sets. minus the novof elerrenG Ya ter ction 5 Veo em ‘ACA 08) = Acad +ace) —Atang) javel = alt tel — fans] y~(@ ned * nCavanc) = cays rca) ence) = NCAA) = NCAAE 74 aacadnac), ane = \aveuclh = jalate| rel —\and\ = \sac land ~{eo | . t atucents ply 10 re to) faa daw of SD students) 20 fot tan, 16 ples. hockey. tt & cfoond that Find he nogf ceudets ples ' seudeny play both - nexthar + ‘ d 3 SY Given af Se norsk pha donts a) myeer” nog students — play cfoctoalt = 20, encry No students play hockey = te = Ace) n(eat) Noe studi play both = (OF a ota) © ntacs) - cava) = na) vir n CEH) = 26 +e — WSF OG \e onl = 2G y (roel vedios ray. £er Ff aete [ oe oe Neom\: = | {eur * \pon| > 2 col \Foel = 2-8) Among, S° “yrudans, US pened pt Sem examiner. S88 Sem examinations IF ZQ studsats panct wf aad neue vranyy paused ww aida't pa wn he “seer esters + etther SE Ne Both Sol Gaver, Torah asf goudank =, © =} + ne) nh) Now seein aud & se = UT 4 Nor students passed f* seme 80 = a ? — qhedan Stan fog elles, 6m | poe (aor Nog [roel = con \roe) F (poe) = cectahee fe (ee 0) (ene je urrde Uy o ot. 739) How many — positive wabegets galt ue) A000 ome divisiole Given thal» stall Mam bert nog) msmben clive FY cae Humbert clvidiole nog qunbes 123 $34 ta French «ond fave take & MG ees a oe eedty +t. 8 We 2000 + te fy = divitble ty AK = nce y4 AB) acana) n cava) NCES) = BES AIELN ay = Mul a students have token a COoUmse ta Spanish, we in Rossian 61 100 studink, both spank & french couree, th y (2 in, Bth Frend, ar ia both Spank > Rossion and = Russians 20F2- studeny WAVE taken COUR hy atte one of sponith ,pfrévicl., Russian . Cov? MAR cecudine = hove dtaben & COUTH in, alk cts Languya. Giver , norog student Spon = (232 =ncs) neg studinb Erench ray = nce) 0-9 student 19 | Rusden > WM nce) nosaj student’ Goth SEF > woo. = a CSF) noel wudens ia GA See oF aos acenr) ne af seeded wth Fee Fe ~ aceon) ro Stl ew able on FEB Fe BOAT encevse®) ACALBOC) = MEAVAM(ADA ACE) # A CADBI AO CANO eacene) 4 acananc) Resutved anludisa . &1 wing Stuchn fave ben lS cours tm a os Canquags = (naanc) « leasnrt pear IDAT =~ RATAN A loo AB AD . Out DEO people GM wale “ports chewnel © vorcteds se a ° aayesteh film channel 2nd A vows neuat channel, 28 — peopl eth Bp and “Teil cohannd , 126 woud, eth spat ronneh p92) wate, Batty chile and — Merarenaneal + ond nerd WM pepe eoakda alk Awee _ chaqnelt Bad! BY} Neg people ashe ont Fated jm watetning any of Re hee, anny! -wr sf Kw Applleectiony of Principle of incluion oo exclusten + ' here tb oan alternative cforn af th Prine of. Jocluiion cewelution that Uregul ta counting Prebleny Jn prontentlan , the cfm can Ge uted Solve rm, TAAL ek cfm UMber gf Clemente a cet thas, | Rave more of 1 propenties Pry Pree sPa Ret Mi be | the subset eoatainiag the clementr that — hove rope, | Pr. Kets denote th number of elements ith oh th, ete | a ha, Pla- eos popes Pea Pi Plas Re be Cy Py “Puy Winiting these quantities ia term of sets .0Se have Jan ® ay =—- Am) et Or, Pa Ba): fate dence number qf elements with Mone gf the” proper Po Ree Mae Pe OB NC tA ey. .e PR). Suppo the noraf eleonants tH set BN. Than 1 fies Ye! pe : N(R Pr Pa MJ EN= [AW ARU-= VAKI. From tha “incluier -ewclusion gelncigla, we tee that, bon NCR PL ik) EN Z Ne) + ENCAR) — SN gat tien a er 3 tgisjen ig sekeo lee # CUIMC AH. --fn)- coe ast ivi’ How many of the inkegend apace FON. By o8y af pubes Us.6 2 Gower age eA UPA EE poe no's ROO Rye AWB, 0,--., 20083 =acey> M+ sorFae pL So Oe ACQ)= 344. NCHA) © Wo 5 eng) = 2209 set oy ; eee yar) EA ager; — ‘ S Cane, AG) © Bt = 39 . ae Woo Hoe Kea cay ETN foe : wiene: GY ACHP) = MY WA (O72 3) eterenor ae aoe) petmes ast Picerent a AU Host Atvaibk | &Y 4,35 HA ame ag Save 7 lotegers 4 Leng 2000. FO) Deters 5 BS toe We tues by 7 oS aoe by air quer, nosgh panes nekl eveatea RT as. no-of aumnions — thek 2 slr no-of- nuenoes cAivnible ey _ me = He ey tse Kooks BSSVor os Late Y oa ey tals» Ai aypin- Ag fans te) Axe Aa = {uss far) Abe Oph, Ag axe mutually dye Kray) sanare g oe OS GAM) TAZ = b> iy AVAL W Aa =. Note - qn, enutually: “Abgpent - A, Ars AS agerify He Aden we =) fad 2 wre ev (a A;) = aso At) le F wy * en CYAi) = utenAr) a Akush, Age famed cage aeetd o> buy 7 Et R28 Sar pg te RA, Ae Ws bee Cee ze fury Ge Qty AUB, = Lures eh | AWALU Ay = Lara ea 9 get AWAD VAUD Luraticiea volesALS AAAs = AGtY lise ta Sanaa Nhat = fe eutgayie'é © Camnanaa.nk J Ayah OCH | Lass. | no CAS “ROS ea enee eo faeh WW, Luton tet 2. fay ava ess eo hee © Cured aoha = x a Caoarja Coe) sheng Coe a@eoes) > Ld en (A04i)- | Ge ee | | tana wend? MO enarr anaes Arey an Ao oS fo ee yg (ane) (waar) O EM) ca cmd = 2 fly - oo ge aCQAr) = per a Lets = OS Hemes gored%) 69) Ax fe, ph, ant 62 Wer What Oe Ay & BxA j axa, ax6 , (ara aara) pst Ret ust tobe Aza, Rh, b= Cuasy Axes [ car7s eat aoe Saed Fo AOL SBD, <3 5 | axa = { ayer cv? | cave 74 SRP? OOP | expe nara s ¥ et 7 EE eprars notation “S' ds defined sc ¢ balf fie clement denoted. g &~ ovdered pais that Di CS) ea ee Belong e Ss * 6-4 2), cau) Cab (6) f (rare 18.5 Q(s)= aosye finpay. fon es} Range of Reloken * Ronge of = sewer OW second atewenky af th ocdened patos thet ein is defined 08 HHE SEE ofArd te censted ty RO R(s)- ROSS { yfax Cre st > ny Br Be ead CHW (are) Cert) Y rey ( mA ety < Operations on Relation | Ss R& S ome HO adosora’ ‘en. 60S Aeinad x aoa welation such thot co * CRUS) Y ep 2RY ew x»Sy Dg CROS) GY Ee ARG and HS Y ay a(R SY e> ay and a$y i wm goRy & *kY ro ps { crar, Qe sUyDY-* ae fous @o 24294 then fra PUG? PMB? DCF) , Bla , OCPOM , 7 ace) , R(Q)? RCPUA) and ghow the , > Plpve) = A(P) NCA) | 9 alene) & RP) A a(Q). “PNA > £ gu) 3 = % ce) Lo nary cad CAE Ree ee & a SIT Given ant, ps £ GAC 2a).Ca3d } m ar (Ga) 4), Curd S ial 3 | pues [ar cud. Cau C32) ude,— pcevs) Fo21,9,8,0h ace = CF eeursh RCO) = L3ru4s acevo) = S22" * 5 aceaa) > Ae 0 pcpue)= Cr) vu ACR) ary Saw fu dC oe) coe CON@? {as ace) He CO) 2 fara : tay € &rand atena) < ate) a C8) .) acnek Se TO eg relation se Lf arw{ nens ee L Cra [eeN eshere naturel nenbe Ruud nd Noe N= find sur ane, Sot yea ge A can, Ga) ER OY CED) 1 @r2S) ge Ce way cea) Cape) Cate) Ee)FF Prepention af 8 binnny velotion ‘mM O& Set \- Reftenive Relation * pm 7 Symmetric Relation 8. hausitive Relation wu dmefleniee Relation S.-Anti- Symmebic Relatien J) Reflenive Relakon weletien BR Wa, see MH Said fh A Gincory Go Grey EW, RK ths Be reflenive Sor everyone = af x EK. Ordered pay AER ear DV The elation £ is Veflemive on the tet @f creak Aucbers sete gf Teal numn, W the yetatien FH Mot aeflertve on the i arluras ReKew Cue) Cad 2 Summebic Relotion ! ‘ i - | A’ lmelotton R=. om Sel Aes symmetee tf vibiiever: arb @ A re J Brave y Wo ke? > ORb bRa. WA Means “Fang one of moked ty ABA any otter af me elecnent As then secmnd cleans & reloted to the fet } The. welation onthe set af ech numbes bb symmetric east Symmebve 2 the welotion Geing «Gtr on the cet ca ‘odd, People But makes. Ye Ke Sym— cmedic on the set af otkRuirvy Lous Cy ie) A gs Transitive Relation * Sea Re ae ta gid we arnt, Sey Cora gee - ARES RA cf eey Hef % gn other aids GiyV EIR, (a2) & (QR) oe GAEF. per may e €R° erry The velotios Zonk = one anon st BV™ eae nee ah ee jum bers wD The «elation “ke wrath 7 te) RSE rand OVE ped and acu then 264 ¥) drteflenive » Relation” ae Co ‘yx te soit be emdiale ye nie Kyte ordered pair Gr) €1R- ep ae CED. AM Symmetric Relation | nr wheter = Wwe te RO seid Ay be As Summetere 4 RY ant RR len PY, Fro ae HY CR exe) The nctation (=) aA “the set of neod cullen i ath » Symmetric > tS) Se Lua aye OY ; ae Lom) nage 0h ee R ft ere CL Ca 1€9,2) Card) CO) ois) CHOGD, Cae Cue Y - Pee eeqeaiee Guay && aa Eicias fe CRD Deve OD #1R Serine taf erdeved pats douan"e BARNS athe gee Ase ase Teglewe, ue sa thE co | sp. te Eaters me Pehle Re LOU, =n Liane) Joa mee in & Gin) €® si) Symmette: YJ ER 7 GER ee LCM) BAN 4/7). IUCHD « COMIC ayo C2erd (0-0) Cra) Can) (Hes) HG) aya 9 sis) ACTS) Gad BCA) the set af — ovdened goons R sabifify syprmette election ts suymmeartric +Pea es CM) E - arenas! Gey) © & KSie) © 2 OA) CI we CUD ER nl eo te ee ea ems gatiyy th trative: x ast sean ite + vw) anti Sgr Rolebr” Chia) Es ux) EF thin BEY cue) C64) EK eerie ney . B® Berithep Pg ee ee sastify nn syenegts melation + se geastutn are wee 8 ts’ eatisyfts Seen recta imeflereRelation meatyin & Dia Graph : ee Relation Mabin: i A aclation “A Afi a” cfinite!” set “a “te 0 Finite set “Q' can be weprenneed Gy matra calle Ahe — aelatton © mabix- Bet ae f aude mh 1 Br { br, Orba,---.60 ¥ be tuo finite “seks containing = TA ERT clement respectively and "R’ Ge ta elettton for A a. * Thea, ‘Ro can be Vepresented KEN matin bo Me= Cry defined os clos y= f % aikei 04 HGS all We elements «GMa eansets of = Lire % MRE: tis and’ O% - gt Ae Leurahs get by x r6q } Consider oi) the velotten R= { B, bs) 7( tba), Carbr) + (Hite Curbs) q Determine tire matrtn « 5 sal Aetrbey oe Oh bah aol (vin). (ves) rey) Cayo) Cea J hy Tie ‘fo \ x 2 |e -o, alo =* 6 a t of A Properties abo Relotion in Set * DB a welation ws 7eflenve, then all che Atogursh entvin reust be 4Va netation 1s agmnmetete so then rth Nefadtes Notsd RB We x Se every tej gl ee cyramette ner A mrelatien mak le ceutncete «te FH A shen HES ST ae ex AM Ap County oS ame rehabton enedin ‘gale we Gire2ey Mie a : A f ae \ 4 VAT ones : os oye { OVk bi aoe nae o Ok bi 4 i 3S as ; 2 ay pane ee SCC Bs way Cd # Gevaph fo Retation + A aelation «defined 88 cfoite) seh 4 also’ © Be 2, wepresentced iM graphically esit the holy of graphy. Th elements § A Ont reprevented by pany cteler called moder, Ther godes ot called eventices / ¥Y Ca rajler hr Lee ance tte a and OF Gy rears ag an are and pat om laermn On SE me ine fe drveckion. dé

ANectiont Wo ai@ar tfinn use gee 8 ame Calnich atents tn howe fot bed eee Ae of, THe EG alr, loop 6 ae 6 o aRa aRG ° are? GRa orks beeACRA , _ aRb AGRb 1.0) Gwentet, ae Cee S paaltrof 279g ). Qiven — relation motrin and brass Wes grey th Sk Sie | Pot Ae. £ 8,664.85 a= C &y (mrad BC) Y UE hae € @&5), G6) Cary, Carrey e j 5 8), othe §- gs \ Oo Y -ar€% -e © c a e es a ° O 06 ey “G1. 6 © ies 1 1 o oO t \ 1 6 o We okve — mnadrin Ys elation atriate Graph Le) ~< Cin PY meokortgsnod -,, eradets A the melatian & caTrenpondtey ototi ' 7 i Ayn pee : erie Geephe op the set. * f ate ge aeeantie Ley 2e0i0 Coasts O18) 222). OD » Gn) Cais), 97,4) 1), 4 ' os eee eee who 4 Srey Be eed Our eee) alee 2ors sles[ Equtlvalance Relostion : % A relation Rom a Sek KX sath to Ge equivalancs welation Yo VEU wegftemtue , ayrnmeteic ANE hramalttve ’ A i nctation Ron a Sek KW Sate te lo parted Slo, welation af ev Nefteave 5 ent oc air eee © ND Equoltty af sutoreta Go onivental se WY |qualtly gh. aumoena am a se Qf read AMenhes | BW) Relation gf propotions —tecing aequiy aledt I a calle ction, ef Prepositions - hey tee Re GUDINY | A= CCU 4.049, CU Cy AA), (352) GD). fovea TR! ay eTUNlanee relation yl at, mee Lad a= {ov, Cho) CD CW) AD AD2 CH) (aia) } roa. | ft. o Me= ilo 1 Te : Se AO) “ 4 Geeayh se ED Feeder. 2 W Reflende: att. Sogped Samana » Gum) eR ee ie co) pea CED Can h EK eG ev eflemve. OH Syms GuyleR 1 Gir) ER Com tay Cay ey OD 1.99 aN iD ~~ Cie) ea) eo ; ca) = Ge)