210test1key - Math 2 10 Section O i l : Test N AME: . KEY...

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Unformatted text preview: Math 2 10 Section O i l : Test N AME: . KEY This test has 6 pages. The p oints per page a rc 4 , 4, 5. 5, 5, 5. [4 p oints] Question 1. Let P be the s tatement "-42 =- 1 C." £. ~~ H ~ ~~ ( / Let, Q be t he s tatement "7 < v'JH).1' Let # be the a tatunient "j: - 7 is t lie only s olution of (./: - 2 ) 2 = 25." r-2 =-S x = -3 T 12 p oints] Question 2a. Explicitly w rite out the power set of < a, {b} >. a a [2 p oints] Question 2b. Let A - { 1 , 2 , 4 , 5 , 0 , 9 } , l et B - { 1.2.3,5}, a nd let C~ { 5,0,7.8}, Explicitly write out t he set (A n C] x ( yl n ^ ). [3 p oints] Question 3a. Construct a I ruth t ablo for (P A Q) V ( P P G -Q p-*6fi) T -T T F F F T r F T F T F T F F :P T 1 [2 p oints] Question 3b. If X —*• V is false1, f ind t lir t ruth value of Tf P*Q T F (NQ)v(py-^)) T T -p / [1 p oint] Question 4a. Show t hat the s tatement /I U (B n (7) - (/I U Z?) n C is false by giving an exp,,c,t c onntaoxan.pie [4 p oints] Question 4b. (,'la.SHify each of the following as t rue or false. If true, give a. general proof. If f alse, e xplicitly g ive a, specific counterexample. (i) True or false: If A U B = A U C. t hen B ---- C. (ii) True or false: If An/3 - An C, then B - C. C = ' 3 / 10 [5 p oints] Question 5. Define a r elation ~ on Z a,s follows: a ~ b if and o nly if 3a -f b is a. m ultiple of 4. Prove t hat. ~ is an equivalence r elation. A^ /s isr * wul-hpk- of [5 p oints] Question 6. Suppose our universe of discourse is the sot of a ll r nts. Let S(x] be t he p redicate ux love.s s almon'' Let T (;r) be the p redicate !1.r is t eachable' 1 Let M (x) be the predicate ".r is missing a t ail" Let. W(j-) be the p redicate "./: has whiskers" Let G(-x) be the p redicate '"x has green eyes" Let K(.r.) be the p redicate "Koko the gorilla likes to play with -j-" Let F(x,y) be the p redicate ",r is w illing to light, w ith ,(/." [Express each of the f ollowing as E nglish sentences. ( 5/ViA^ V^f'^TKJ"^ <Mt fl *»)J+ a CAT n*s r^ fr<>!} CA T ' 5 A ^ F( / y , ,,; is ^ c* v*//;/ 1 ^) G i wm'-f f\*kt 7 ...
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This note was uploaded on 12/07/2011 for the course MATH 210 taught by Professor Staff during the Spring '08 term at University of Delaware.

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210test1key - Math 2 10 Section O i l : Test N AME: . KEY...

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