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# hw4ANSWERS - Neal Whittington(whittin3 Tuesdays at 4:00PM...

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Neal Whittington (whittin3) Tuesdays, at 4:00PM AD9 CS 173: Discrete Structures, Spring 2010 Homework 4 This homework contains 5 problems worth a total of 50 points. It is due on Friday, 19 February at 4pm. 1. Set Operations [16 points] Suppose you were given the following sets: A = { Piano , { Violin , Viola , Cello } , Guitar } B = {{ Flute, Piccolo } , Cymbals } C = { Piano , Flute } D = {{ Violin, Viola, Cello } , { Flute, Piccolo }} List the elements of the set for the following expressions: (a) A D { Piano , { Violin , Viola , Cello } , Guitar , { Flute, Piccolo }} (b) B C (c) A - ( B - C ) { Piano, { Violin, Viola, Cello }} (d) A P ( B C ) (e) ( B D ) × C {{ Flute, Piccolo } × { Piano, Flute } = {{ Flute, Piano } , { Flute, Flute } , { Piccolo, Piano } , { Piccolo, Flute }} (f) | P ( B D ) | {{ Flute } , { Piccolo } , { ∅ } , { Flute, Piccolo }} (g) { X P ( A ) : | X | is not prime } (h) { X ( P ( A ) P ( B )) : | X | ≡ 3 (mod 2) } 1

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2. Euclidean algorithm [4 points] x y r 837 2013 837 2013 837 341 341 155 31 155 31 0 31 0 gcd (837 , 2015) is 31. 3. Pseudocode [10 points] (a) Trace the execution of func(a, b) . a b m p return 2 5 func(2, 2) = 4 func(2, 1) = 2 32 2 2 func(2, 1) = 2 func(2, 0) = 1 4 2 1 2 2 0 1 32 = 2 5
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