Quiz for CMSC 250 - Discrete Structures with Plane at Maryland (UMD)

Quiz Information

 Material Type: Quiz 6 Professor: Plane Class: CMSC 250 - Discrete Structures Subject: Computer Science University: University of Maryland Term: Fall 2002 Keywords: Provided ThatSquare BracketsCombinationsCalculatorsSubstitutionInfinite SetsConditionalTotal NumberCmsc 250 QuizPropositional

Sample Document Text

CMSC 250 Quiz #6 ANSWERS Wednesday, Oct. 9, 2002 Write all answers legibly in the space provided. The number of points possible for each question is indicated in square brackets { the total number of points on the quiz is 30, and you will have exactly 20 minutes to complete this quiz. You may not use calculators, textbooks or any other aids during this quiz. 1. [30 pnts.] Disprove by counter example or Prove each of the following: a. The quotient of any two positive rationals is rational. ANSWER - true - proof by generalizing from the generic particular: 8x; y 2 Q+; xy 2 Q Proof: Let p and q be arbitrary in Q. 9a; b; c; d 2 Z; p = ab ^ q = cd ^ b 6= 0 ^ d 6= 0 by de nition of rational. a > 0 ^ c > 0 ^ b > 0andd > 0 by de nition of positive in algebra. p q = a bc d by substitution. = ab dc = adbc by algebra. ad; bc 2 Z by closure of Z during multiplication. bc 6= 0 by algebra. Therefore, pq 2 Q by de nition of rational. 8x; y 2 Q+; xy 2 Q by generalizing from the generic particular. b. ...

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