06Fe1s - NAME: S’C’gufi “’13 Prof. Girardi...

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Unformatted text preview: NAME: S’C’gufi “’13 Prof. Girardi 10.03.06 Exam 1 Math 300 MARK BOX POINTS 25 3 15 15 INSTRUCTIONS: (1) The MARK BOX indicates the problems along with their points. Check that your copy of the exam has all of the problems. (2) When applicable put your answer on / in the line/ box provided. Show your work UNDER the provided line/box. If no such line/box is provided, then box your answer. (3) During this exam, do not leave your seat. If you have a question, raise your hand. When you finish: turn your exam over, put your pencil down, and raise your hand. (4) You may not use a calculator, books, personal notes. (5) This exam covers (from A Mrtsttt’on to Advanced Mathematics by Smith, Eggen, and St. Andre: 6th Sections 1.1, 1.2: 1.3, 1.4 . _________—_———— Numbers: 0 real numbers = R a natural numbers = N = {1, 2, 3,4, . . o integers = Z = {0: :1, :|:2, i3, :4, . . o rational numbers 2 Q = {q E R: p, q E Z and q 7E U} Throughout this exam: (1) P, Q, and R are propositions. (2) P(:r:), Q(:t), and R(:t) are open sentences with variable 3:. an: em. fl ms, E: 2:3 mp QIFEEEEQE < Eafi EA Infrahoviqhflm: k) :mAHQim ohmimog, .EAHE/‘SAHQZVZA .QEAHEEEEMMAJ _m,..[email protected]<m:\3 “ma/533$? .mfio/‘m: xi, STE: 8:5: _ R1, I:<&>5<n.: E9 SIAHQMLGA E “Ha; N» 32¢: a» 53:22: .3 Ioawimigb, New»? 31y}, .m I .m E Sam “9 I H 3.35 .uma 32.5335 no H :EEEmrSrm an .mflw. éofimho .Eififii maflofio .E 2“ fl 5 2” ggg+ 8. 3 9:53:95 an. EEO—UV 9:5 .3 .5533 :55 MadeEwn—u T53 3390209“ 3:: waflzflbfluu EB SEEEEE Egafiuowwi ififlafiugwfi $6523.38“ 2302285 ".Efififiabv Amazon. mafia—5 awe—2:3 a with 3 swan. ES: 3: Bob m I 4. f?— BEmE 05 E 2: “ma I H Ema—ESE EU 0 mud—H.— . mfia g 3&5 35:3 8 a £3 iaE 2: E .a .4“ Ba am :0 . I IE EH HE HR flfl flfl flfl EB flfl fiéwd?% m... alum . Emfiaymv . Emflamu . .haifimv. :eifimza :aififi? Tm .H m9>m1 Tm .H 82m: .528: H a...“ 139:” n: . in. W m7; . 29:3: . 20:7,; . 203:2. 2m<§>mw 25/95; :m<9§; Zm>o§i 2026“ .H an; 33: g H Qicfimi :oflmZn; .2“ 3 w 3055:: mm: £6395 mEH. an,» 2F an i . .m>:_mom.mb=|8 E I’lmuampnou £3— xnfin 2: E :c ,mw Ea an EU - p a _. .. .c ...5.WW1I We; at O A” an .3 ,. IL: fl 3 325315 Mag .5 3 E25??? fl :3? «:35 an... E 2: "ma 1.3 an DO a max. at on”? at .m—. .1 .5“ t .3 x .5. x. .3 # gr 2* :3, 2.1 .01 ‘my Hug. .Dlr .mi .wba .m,» .m,» A,“ .820 >420 9:.“ .026 .532 :33 mm: .m 2. Make a truth table for the propositional form [(~P)=>Q] V WAR]- P Q R [WE—me v [a Am I: r F T l: T“ T F T T” F F T“? F F T 1: r: r F T F T” ' T F: t T _ T F PM T E ‘ *r LP F F”: F F F 3. Show that P => Q is equivalent to (N P) V Q by making a truth table and than writing a sentence or so about how you are reading your truth table to come up with your answer. 4. Is the quanified sentence true or false? Explain your answer. 4a. (W: E R) (33; E R)(m + y = 0) circle: or FALSE Fm: *‘< a “a :_: twill. K. :50 '3- ‘ l? i} 4b.(3mER)(VyER)[$+y:U) circle: TRUE or -‘HFALSE) (:l'Y l£)(“.)lus ly’wj r—O) EEK 6:5» Mia-qr? .,-rilr<,~.:v_u_ :0) AI; elrufii ; <3 :3 “£5 e {E‘flflfi} (XV-{#0) ML +ru£ C- C 9-9 li'v “(a 5'72 , 1.: ‘r-"V L I? T?\fip f (Lynn. N 4-- :- Y 4' "T ‘l‘ ":- l”! f _.__ r ,.. \ '1') 5 =5. —i -- ' U! (and explain below) (and explain below) 5. Translate the following English sentences into Symbolic sentences with quantifiers. .f’, . Um the notation: U = Universe = all stones P013) = :r is a precious stone B(m) = a: is a beautiful stone . (Box your answer.) 5a. All precious stones arc beautiful. mg a} [ M :3- sou—l 5b. Some precious stones are beautiful. r3“. M {Pm A may] 4 L K 6 6a. To help clarify the order of operations, add some parentheses to: (VmEN) (<xisprime /\ 9:752): misodd ). (6*) 6b. An English translation of (6*) is Answer: affixik {pa-m: "f.;_"r_ -' v- x 1- 6c. Symbolically write a denial of (Vy E R)(El:r: E R)(Vz 6 Emma; = xz) Without using the symbol ~. \I. a“ M\ A, (we Mfg «r was; a {M (“I T ,K i_\_ g If:er "" Clv \f'é!_) .\ I t d {K Jr I, 9y 3‘ ’U .9 l| \ N . ) A. l ("I 5 lg l kt!- r x /' . m k r u I 1L3" 9 A r '3‘ c A. {V J m :r‘ J ...
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This note was uploaded on 12/13/2011 for the course MATH 300 taught by Professor Staff during the Fall '11 term at South Carolina.

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06Fe1s - NAME: S’C’gufi “’13 Prof. Girardi...

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