{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

07Ff - ~14.o.n4_15,ug&¢e— 5141 9101—34-43 i i 4 i...

Info icon This preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 12
Image of page 13

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 14
Image of page 15
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: .. . ~14..o.n4.... _15_._,ug..&¢e— . . . . . . _ . +5141 9101—34-43 . _ .. . . i i 4. i | 5... 5 [ll _ ’/r5 i_.._ g i 2A; J } Ella—nus Wuem Illa-S numbafs j; 441 25 . (3'56 €01“:l’lcij-Fill'inblflaxksw‘fl‘HA'S 19mm balm 40 Mile, L‘i’awjrflojy , _ _ .mck...}g’r{t.r angel and. migmncg- . . s.§[(?=>a)A (61%)] => ___'_ ' 1.2.1:~(P=>a)1 4% 2.i[?/\ (Mml a; __ r3. EfiPVQHR] 4‘3 ___.__ 5.i[~?£> (61 M90] <=> __ H: E(PAQ)%R'} $9 _____._ a}. g[ mam] _<’e=>_ __ *5, [Péfiavmj ‘1’”) 5. {L PA (am)? <2; _ .14- _[ PéiaAR31® _ ;. ELM (am: <9 M - [1.93019 Pm] “<3? inlt Pv (awn @ __ if. Wax) Poo] <2fl> ....____. K. 11: PA (a A331 ______. lqflUEifl Mil ‘1‘""> __“_._._, “é IT.— HPx/a) 3 w m: _ $0 m (M601 {:25 __ «ark/Defianjan‘s Law. _ H. ~ (PMUJ 4:) M__ W AM 61'1..A.ND H19 ianflloézrjfillinblmks wifk: THE or FfiLSE.__ m! (311M903 za (3a) m _ 21,§{3x)__P(x) _ :3 (3%) Wm) .. Lie) goa%u%13)_ 911 m gm. wé+lrl...a_.._....._I_5._ err 15 NOT .. PéQ _,__.______._____ . c-LuiW—Qwi M Q?) P ._ 25.9351 ._._________ fifiéwémflwwfio {9‘50 1% (“’13) (id) 011* ,2?! ¥ ,5 in: in Mia; may: : cowensE er Cqumfisfiiyia, 2%,; We ant ?=>a «is («m—"Mm 25.: TL?— _ . $961 “Ls 6L. =3. .? - “MMWWMWWWWW 31—31» 0:91): i “151 5 .5:13.fl?¢$)h(fl).w%)(MN Hap) => 5%) . P .. C'r... (M)A.._(PVR) r4. (TA~Q)..-*->R . (PAa‘) AR. u‘ (h; GOMHR) oi (~22) A (w a). . I. (New R .. __ 0.... .i..P-e>R)A(Q2>R) Dub?) v ma) 3’. P 25R I P; (PéQDA (GI-=3?) E; P A ~61 ' K- Pa>~él <9. CHRWKQ E..,§LMQ).V..._(.PAR)..__. 'L-__(?_.A.~R).=>r~ea. ....’R.. .(MLWMJ '- [I] 5L2. EFIBC. F pg“; 1? 9%.. i | g E l. ,_ .. 9.. _M+{¢»_.£¢M~z ‘fo 1%: n u - 2' .Tf'KQPQS‘EZJIlea-JHfiW?" 1-4. Hat-M01935 ) F . fikdrcfim at _. 50w Mir—L _ 1> F1 d F“: mm: dim. S :‘\w_3r_l .. ' Ee— "aj " " P Q} R ___... ..._.:...._,-...._ _fi. ___ ........_._.._.__........ ._,.-_... ..Ofi% 'o Emfi‘mgg fi-E’sécfixifl m Ni?“ Hfi r" I i ’5 a. {WW _ .I ‘J. [I] $419er ..4...mm.m . '-<. mamW, 13.4535“? QELANFIFIEESL ' . flu . . LL?— Mnisiav‘m. m. dams Mm.) _. at. £5 gram-fiatcimss Fix} == x 5.2a... {iu».-n_ :fia—fi: Box You! firms war A” mafl’l. daSSi-‘b are 7AM”) . i s i' .i.. mqu 530.9583 aft. ‘F‘vbfl . 1.. i g E i cofisial-Je‘r‘ fie. fF‘OPgsu‘kéfld- ng‘m _ I - FfiLSE I 1-...(C‘frcL afimprfifitmma I W R )_ (3.35111) M 0.). .. GD 4.; m a; a . 3. TRULY; .. of. 1%“; WW) i I ! I s. % 09m. 14 m emu—r? afh?oPr*W-amwer\ i E a I i 1 [ll §I.5 4+ [2; (savanna, 5/5 l l E I Iii. “his Page). {not} Mt. .i-Eloofs‘aG’m Problems with this title throughout this book ask you to analyze an alleged proof of a claim and to give one of three grades. Assign a grade of - i i i A (correct). if the claim and proof are correct, even if the proof is not the _ _ . . ._ . simplest or the proof you would have given. '. C (partially correct), if the claim is correct and the proof is largely a correct claim but contains one or two incorrect statements or justifications. .a F (failure), if the claim is incorrect, the main idea of the proof is incor- J rect, or most of the statements in the proof are incorrect. l i J Justify assignments of grades other than A. Whenever a proof is incorrect, _ I explain your grade. Tell what is incorrect and why. .___._._. .. _ ._ Supposex and y are integers ._ _. _ _. . . Claim. If): and y are even then x + y is even. . . “Proofi” Suppose x and y are even but x + y is odd. Then, for some integer k, x + y = 2k + 1. Therefore, x + y + (—2)k = l.The left side I l i l E the right side, 1, is odd. Since an even cannot equal an odd, we have a . _ __ ... __ ___.. . .. _ l ‘ ' of the equation is even becau'se it is the sum of even numbers. However, contradiction. Therefore, 9: + y is even. I I _. ___________ __ _. l _ _ r- _ _ J l ,_ _ _ __ _ _ . __ _ ct. _.. . ._ _. - _ __ __ ._ _ . . . _ .. l _ T _ _ _ ! i ' II ---------.... . . _ __ _ ., _ ..i ...... .....___ a ._ , _ ,_ _ __ ..._.._..__ _ _....._.... ........._ ' ' f 1 . Claim. There is a unique set of three consecutive odd numbers that are ! ail prime. “Proof.” The consecutive odd numbers 3, 5, and 7 are all prime. ' Suppose x, y, and z are consecutive odd numbers, all prime, and 2: ye 3. Then y' = 1: +2 and z = x + 4. Since it is prime, when x is divided by 3. ’ the remainder is I or 2. In case the remainder is 1. then x = 3k 4- 1 for someintegerka1.Buttheny:x+2:3k+3=3(k+1),scyis -- . - . .. u not prime. In case the remainder is 2, then x = 3!: + 2 for some integer k z 1. Butthenz = x +4 = 3k+2+4 ='3(k-i~2), soz is notprime. In either case we reach the contradiction that y or z is not prime. Thus I x = 3 and y = 5, z = 7. Therefore, the only three consecutive odd primes are 3. 5. and “i. I (Lib) r miss... .L'EM [as _ 55% .5. nine. W.c-u~iitt€ .adql._mmheris _____ “‘6’ I .. ._.i.§j.5,?}_ MB.any}... 3...}.11}._l_l_3)_“.51 “$.15isxn) ii} . .2..i.._..L£. p. ésrtanims’, ..._.nn.m}2.ert.. f’lfhgyn .. w 3,; es. the deem algorithm sin.» 2. (dividing... .12.. a) (.‘v’n 8. i 3. "2.2 ) (if 5L0) 1,1,3-) {— rx..:.: .3 ill 1 .5. CMsidar. proklems (5'1) and. (552)- . 1 1 51.15 #40 F . CéL‘hPS‘t WWW ?/ '5 I _ . .. __!_+hr,n__._£iflnr __ K...a.r:.__ __._.-L.S __ .. _. " Lama? . ' {is " «e9; Z)("a¢=§j__. QW'OB. .. is Emma‘ml .<-—-—>__.x .3 .4; . . ._ .. i E i . L . .. . _....._._. ._ ._.. _ . r _. _ _. (5 . ..) LQJT . (5*!) .n"-‘-'-'-"" #3? J g: m, __ __ (f5 _- a; _. .. __ . _ _. ._ I mom—ww— v-mv o'u-m— W‘I—‘i-‘v-vH-u—mmlm P... ' . ' i . I . . . I ! . ; i ! i .- _I .' 4........._._......_.-._.._......_.._....._._. 5 l : . i I I. I [II 44:6 Sl’"""‘f) 0" ,an‘l Exam) x!“— qu M 5 p E LL ~42: 2c! __ Cmadpr...g1v[1(m-S “‘0 ((9.793. _. . i (C271) §L¢+__?¢_§Z, 17E. icing; .th dwidgffléfflm) .,_. Ham __ _..._Ua'2-) _. gm: _ __ [email protected]fifimflw I 4a.; by: .1 I. ad 1d.» _ n W8.” "A. .does..._.n_of'__._d_iw‘d.&.._..a..__w .91..dn:§_...n._9f._...di!i¢l¢ .. . Ram/ll {gnawing Mhirl’imi miofinr-QS . .w . A; <?>__L3&5£2_('x...= 1M. .. . Ea _ .; WED. 9:) (35:92) (-9: _=_;;§_._—_-I_) . _ -9—5. afiaz 2.. __ gm gum-m A. __ ._<—-=> ._ @161 ..__%%'>' (3.}2§223 M . ' .' _. _ gtfl' . (L¥_r3jf_jw. 43, g.u;g_m£_____b;__ i ! fist _ 545m AWE-awa a.ng ._ 1 u. £5 am 5% «EM (Ma—0 ?_ 7’}. 3(a#2..)....gm W. w, MVM wvmg m MW in 1%; w: w ) .. [ll 3%“, fr.» Proch {of fibé Ilullllrllsillllsliqilli [115...]... .... lliinll.if{lalsLif§tlJ!.illLlllilLIlillt l | glfi‘ #15 F p §l-Ur # (8’6) [3/15 Vobfems__ (7”) muL Hal} . (4*1JIF0...F my». new. 3: (em—~23 -= n"<€n*13; (em . . a (7’2) éFor acne-k m8— N : } Ea‘nafipfe, a; M¢W€@‘¢J 3 m . ...S 55 0~ $947991 .4489: +900 propwfié—fi I ‘For ml{_..h.£ N,_. .LF..Y]£ S...) “H E. SJ §+5wn .S 1N: . Ii . iUSI' +iu. Ppfihafiyfib Mmfiirewdimi . Egg 43) {m} no’c lacrflx. 5% ) (7'39 M (4"?) i I ' __ m... [I] $t=av~ FM rm? gar #7- Ill ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern