hw4-soln - CS 173: Discrete Structures, Spring 2010...

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Unformatted text preview: CS 173: Discrete Structures, Spring 2010 Homework 4 Solution 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 Solution: { Piano, { Violin, Viola, Cello } , Guitar, { Flute,Piccolo } } (b) B ∩ C Solution: ∅ (c) A- ( B- C ) Solution: ( B- C ) = { { Flute, Piccolo } , Cymbols } A- ( B- C ) = { Piano, { Violin, Viola, Cello } , Guitar } (d) A ∩ P ( B ∩ C ) Solution: P ( B ∩ C ) = P ( ∅ ) = {∅} A ∩ {∅} = ∅ (e) ( B ∩ D ) × C Solution: ( B ∩ D ) = {{ Flute, Piccolo }} ( B ∩ D ) × C = { ( { Flute, Piccolo } , Piano), ( { Flute, Piccolo } , Flute) } (f) | P ( B ∩ D ) | Solution: | { {{ Flute, Piccolo }} , ∅ } | = 2 (g) { X ∈ P ( A ) : | X | is not prime } Solution: { { Piano } , {{ Violin, Viola, Cello }} , { Guitar } , ∅ } (h) { X ∈ ( P ( A ) ∪ P ( B )) : | X | ≡ 3 (mod 2) } Solution: { { Piano } , {{ Violin, Viola, Cello }} , { Guitar } , { Cymbals } , {{ Flute, Piccolo }} , { Piano, { Violin, Viola, Cello } , Guitar } } 1 2.2....
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This note was uploaded on 11/09/2011 for the course CS 173 taught by Professor Erickson during the Spring '08 term at University of Illinois, Urbana Champaign.

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hw4-soln - CS 173: Discrete Structures, Spring 2010...

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