old-quiz3-solutions - CS 173: Discrete Structures, Spring...

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Unformatted text preview: CS 173: Discrete Structures, Spring 2010 Quiz 2 Solutions There were two versions of the exam. This solution sheet contains the answers to all problems from both versions. 1. (4 points) Mark the following claims as “true” or “false”: (a) There is a one-to-one function f : { , 1 , 2 } → { a, b } Solution: False. (b) There is an onto function f : { a, b } → { , 1 , 2 } Solution: False. (c) If f : Z + → [0 , 1] is defined as f ( n ) = 1 n , then f is onto. Solution: False. For example, 2 3 is in the co-domain but not in the image. (d) If f : Z + → [0 , 1] is defined as f ( n ) = 1 n , then f is one-to-one. Solution: True. Each input maps onto a different output. (e) For functions f , g and h , if f is O ( g ) and g is O ( h ) then f is O ( h ). Solution: True. (f) For functions f , g and h , if f is Ω( g ) and g is Ω( h ) then f is Ω( h ). Solution: True. (g) For any A ⊆ Z , there is a y ∈ Z such that for all x ∈ A , x ≥ y . Solution: False....
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This note was uploaded on 11/08/2010 for the course 173 CS taught by Professor Fleck during the Spring '10 term at University of Illinois at Urbana–Champaign.

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old-quiz3-solutions - CS 173: Discrete Structures, Spring...

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