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MDsolution - Math 8 Midterm Fall 2006 Instructor: G. Wei...

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Unformatted text preview: Math 8 Midterm Fall 2006 Instructor: G. Wei Name g Discussion time (CiICIG one): 8am; 5pm; Your Scores: 17 2. 3‘ . 4‘ .‘ 5. Your Totai All questions have equal points. Continue 011 the back of the page if you need mom space Good Eucicl in Make truth tables for the following 131 opositionel forms: P=>(QVR), (PA~Q)=¢>R. Then determine if they are equivalent. flirt-154 Ta H M Prawn/K) 4M? (pn~&)#/~Z [mm fem, 6'th Vafwoy $17 w. ezw‘W/wf. 2. Negate the following proposition and simplify so that the no negation symbols appeal? Use symbols only. The univezse is all integers. (Vn)[n > 0 => (3a)(3b)((a > 0) /\ (b > 0) /\ (a2 + b2 m n))]. 7/,5, 4'4 l7¢1M/Mf i; (Ufl)£/‘-(H90) V[94)[25)((k?v)n(é>9)“(671+élzm))] H; eta/Mafia? 2’3 (2 n) [ (w) n (WWW so) v (Leo) V (a WWW 3, Let {ACl : o.» 6% A} be an indexed family of sets and B a. set‘ PIOVG that (film—B: flog—B). QEA aEA {Walt we to: x e {/2 nan-(s '16-‘41 “‘5’ ken/49¢ «ml x693 de- a a” “4% tnwwfl ‘Wl X‘M 4. F0: natural numbers m, n, prove that if mn is add them both m anti n are odd“ KIWI: Wt W” /WW. ii msza/WI;#M If #4 PM M w. rmf ova/5?! Mm. tat/w M w 1,, w ext/em. ‘ If! m 7/5 Mm J m: 1/?“ h {om vfiwrk 5% PM =2b1:2&u)a WM Sfmhwf] I 14 is we», “’2‘ mm «"4 51/24. 5‘ Show that for 2L1} natural numbers n, 12+22+32+"M+n2=ML1)6(2fl_ 1; ((+1) (2~1+r) é flk; l/WlX— ’5' fu—y [1 I mfg “171/ 549 w {C Wu {w #141 L 1 L z + 7, +é +141 +0440 -.: [I ‘1‘ 21+1L+~+14LJ 7L (maul ._, M (W) (anfl) é] Maflubfifi j Z + (“H”) AWWM 107+” [ ‘lerj ~+ K (574—!) _ 5 “ : 07+” :3 flmfiv “"5 6/“ fiw MA (.5; W71 / 1%; +339 ~+ 1/, I :3 WM” 2%“) 74,1, M!) /7 My ...
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MDsolution - Math 8 Midterm Fall 2006 Instructor: G. Wei...

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