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Unit 2

by: Jaquelina Rodriguez

Unit 2 MATH 1301-006

Jaquelina Rodriguez
GPA 4.0

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About this Document

Includes 2.1 2.2 2.3 2.4
Contemporary Mathematics
Sonja Godeken
Class Notes
truth tables, venn diagrams, Subsets, set, notation
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This 22 page Class Notes was uploaded by Jaquelina Rodriguez on Sunday September 18, 2016. The Class Notes belongs to MATH 1301-006 at University of Texas at Arlington taught by Sonja Godeken in Fall 2016. Since its upload, it has received 10 views. For similar materials see Contemporary Mathematics in Math at University of Texas at Arlington.


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Date Created: 09/18/16
Math 1301 ,l j::1 Set Notation Obiectives . Use setotatioto identiand lisvarious typessets. . Recognizequivalensets, equal setsandthenulset. . Determinethe cardinal numofr a set. . Description =) well-defined in words Roster =) list elements inside { . Set-Builder Notation => {xI Read "the set of x such that" Example 1 Costa30-Secondercial DurinSuperowl Years in which cost of g 30-second ad E was less than c '97'98'm'0',02'04'0s6','0'09'10'lr.5 million. Year rl: If b,c11 : 1r ] MOre tl-un g .1 wr r run \\ ?oBrollioi\r3 Example 2 ltrrcrr\tf: {January,February,March} 4- Firrirc 3 hnunth\ ol the tltfir qu(IYler 0i-\v\.(" ';rn0v\w\\ \n hrrr 9tqr 'r 5 e\tw\errrtr Examplecq3cr\rv\o*f Odd numbers between 3 and 13 -6orrer: ItJfi,,\\J -k+ brlrl0triI x\x E orlo\l 3z x^t4 S\nrrt 1 Ccrrrr\rnru+ Ll Example 4 The set ofWhole Numbers - Roltr-:, I or \ l2ri i LI,"."] - Stt b,rr\o\trn, E Wno\t I n \X Se t of urho\t \1C o?,,) 1"ot1 u 0rll2r3 t 3 Example5 LetM be thesetofnatural numbers greatethan 5 hoiKr: t b,1r"o, "-"3 Set Bu\\t\trr x x t ut\yu\lJ I \ N Stnlernher 1" Example 6 {L,2,3,4,5,6} n = u Dt:tfrhr:"St,t o{ (rnt 106i11'uvu\ Set Sur\tArr:,f x\e Norturul\lJ Example 7 {xlx€ N and7 <xs LL} hc\rer: LA,1r\or\\3 D(ltr\h(a S<1 ot no*\K.r*\ n.Xe\l V1: q Equal sets vs Equivalent sets Al@ Set A: Museums in Paris -t B;il'ilJ'J.qf,r*f** that have more than 2.5 -3,I1lio,ialcrlleryofAnbn,Dc 4Tdeodem 4.95LonUK. million visitors. --5ofln'Mu*mli4.81NeYoN-- r-NatCalleryl.l$vu,ily __8:[,vd'9_ _19,,-grjlT:___ 9nU.d'Modme :.98Puh. Ilrdce Set B: Museums in 1MueumotMmde:.S NFYoNY. Soutu/,!$s@tr. London that have more than 2.5 million visitors. rq: tg,1i1) 2qu,1\? NoW'il Llr"] 13, f-\ r qt\ t,qu\v0\tnt? CsqYna I---$)rru\ Set C: Museums in New York City that have more than 5 million visitors. 9.MusR Modeme prudo ".,.PuiFrrnce . 10.Nm:fMod@Art29: NewYodi.NY f=z ] = *nn[.,i\, SunThcil.xrp4.r A Example 8 U = {4,7,9, TT, LzI g = {4,9,121 B ={9,12,4} g= {7,9,lU h$,C Zquc v c\r nt L Sclr1n< [qyg\n4rA\S ) €qua\ fl= B L ?-xuct\q\0nno t\nYrun'ff) r L 3 : q \^c c\enmn* \vt , .0& Srtr\tv^r t y'C.' \t2, o'or;, L.!$a \?\'\toq rt 3l, /.) gt\ttl trun n. , huturuN dhu{Unnl1 jcouriirng ',1,2;3 /) \ .-.- //' ) \J\^o\(, --e() \rC,tttnilb \n\t(t)" ' li,t)3,rlla fiot'\o) Rtct\l Math 1301 i1 ^ Subsets Obiectives .ldentanddescrisubsets and determine numbers osubsets.ct Letset A ={L7,lgl Suu tet: Ire7, I rqJ, Irr,r13 nCnl = Z rn Sub:e1, q U = {3,5,71 A = {3}lsA a subsetof U? 9e: g = {3,7}lsB c U? ("asubsetof'} qe J ts c u? 0 9rl lsU E U? LltS Listalthe subsetsof U: 5,7j ,].,S ts,sj ,t ,[-s, )f_t,5,13 3j , t53,ltl t n (u\ :t V1SUhS 8 ' $st Subsets Numberf Subsets {} {i l:20 {n} [" ] {} 2:21 {n,l {o,} {o},{a} {} 4:2x2:2? {r",, la,,cl lo,l,{o,},t,.} {o},{b},{.} {} 8:2X2x2:23 Number of subsets ina set with "n" elements isgiven by 2n lropcr lel= 2n-l g Tom} = {Jo€, Maria, How many subsets? B : 2t ListProper subsets (symbol c) r- mc\ttq3 t Joe i lorn1 [foe, tnGrlo, Jovn3 [;o.3 t rtonu3 ffonn] L j How many proper subsets? 7'-l .1 Expression forthe number of proper subsets ofa setwith n elements is 1^ * \ Use set A= {2,4,6,8} to answer: How many subsets? ]q ,lG How many proper subsets? 2.{_\ -15 Summary Differencebetween a subset and a proper subset and lisa nylall Determine the number of distincsubsets ofa ny fiiteset Math 1301 ,l ,--1 Venn Diagrams and SetOperations Obiectives relationshipssetsngtrate Determine unions and intersections, complementsets ACU [' =; inU but NOT inA A, L\ U = { \sr}-13,,5,b,1$} A={i,l,u1 1 A' - {L t5tbiqtbl AandB ACB are DisioinL---"" (a) Most A =B ----'--* "--.qOffifnOn, usedto show many relationips f :A* B -lL= h nl3 E =CY+uB)' ANA: 5- L t lersacftuy.r ",.,qvrtl,, rvr hoth Kff U A B I lnl ilr IV ,4uS tu ntov4 r,qy,, tr:tn1t\trng \vrlrUfv1 kra- UA fr r trlilr w A*8 A U B- f ,.ocd+3urt t^:J A $= a,h3 n I Ir,rnru) n(AU B)= \o ntkt)th[B) A $= t-h, Ctt twJ w v1T B:T Y\L Fe pB A =setof occupations with2008 employment atleast L00 thousand B setof estimated = occupationsin 2016 at least 300thousand 1-> ffrOO\rlC+ LyO\\f'vg0$UQf CC.rr+\\\ut^ A = {1,2,31 3={4,5} Ax B = {L\lL\\,11,t)IfrLt\,1}15),Lj,V)p,s} V1t0) nCn'6)' 1 n(A xB) = b 'YtLt5)= )- B xA = {tq1}),LL\rz),ti,r)71r-),t5r3) } Yxrt\^ots lsAxB=BxA? NO -tqu,uu\rnt (qu(t\ Summary Draw a Venn Diagram and representsets? Explainrelationshipsmong setsusingthe terms: union,intersection,mplement? Understand and use operationson sets? Opro|, Math 1301- ,il A 3-SetVenn Diagrams and VerifyingSetEquality Obiectives . Designldranduse3-set Venn Diagrams *Verithatsets aequausing Venn Diagra ms U How would you describe region I using sets A and/or B and/or C? f,E<ffi6" (,' Region ll? C U ns)-C o. tF B)n ^ RegionV? CAn(rnC) Region Vlll? CAn B nC) ' - On(nut)' lx.i" B I tIt IIT rvVvr /i\ /IvXvl VII / L\ -,,'IIt .VIl./ ,u, ARegVon RegiVYI RegionsB IlI, lV,Vl, I /II\II v IVVVI .\"'-/ * AUC BUC AwBwC (AwBwC)' RegiIIl, lVIVII RegiIl|ilV, RegioIll, lII. lVRegiVIII vvr.n v, vrr 3 ll VII What's A n B L L\,1,103 ? (e-rn)vc ,trBuc)'? 1-\rB rL\rtr1r\0, \13 t.bra,rQrt5J AnB nC ? B-'(AvC) ? I q,qj Ir,5r\ij DeMorgaLaws t.teflB)'=A'UB' 2.AU8)=A'nB' Prove usingVenn Diagrams? CnnB )' A'u 6' tnuB)' U YIII Show that Av(r u C)' - Aw(tr'nC') FlutB\)tL_ 6 v t R'hC) C b'ot' ) ':. GoId SflverBromeTotal Coun"'"'Mcdak Mdak MedalMdsk l Countries that: UniStates Il0 China 5l 21 lo0 A = won at least 30 7t gold medals Great Britat9 r3 l5 Australia t4 t5 l7 r6 r5 4l France l7 B= won at least 15 South Korea t3 l0 3t l0 l0 silver medals Ukaine l5 l0 C= won at least 10 ource: UniOlymCommiltee. bronze medals Construct a Venn Diagram to illustrate the sets A, B and C. U YilI Crtt-o,+ nnrry; vIII Summary 'Can you design and draw 3-set Venn Diagrams? *Can you verifythat setsare equal using Venn Diagrams?


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