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quiz2 - CS 173 Discrete Structures Spring 2010 Quiz...

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CS 173: Discrete Structures, Spring 2010 Quiz 2 (Wednesday 17 March) NAME: NETID: DISCUSSION DAY/TIME: This quiz has 2 pages containing 4 questions, totalling 20 points. You have 20 minutes to finish. Showing your work may increase partial credit in case of mistakes. 1. (4 points) Mark the following claims as “true” or “false”: (a) There is a one-to-one function f : { 0 , 1 , 2 } → { a,b } ALTERNATE: There is an onto function f : { a,b } → { 0 , 1 , 2 } (b) If f : Z + [0 , 1] is defined as f ( n ) = 1 n , then f is onto. ALTERNATE: If f : Z + [0 , 1] is defined as f ( n ) = 1 n , then f is one-to-one. (c) For functions f , g and h , if f is O ( g ) and g is O ( h ) then f is O ( h ). ALTERNATE: For functions f , g and h , if f is Ω( g ) and g is Ω( h ) then f is Ω( h ). (d) For any A Z , there is a y Z such that for all x A , x y . 2. (3 points) Suppose that f : A B is a function. Define what it means for f to be one-to-one. Be specific and precise; do not use words like “unique.” ALTERNATE: replace one-to-one with onto. 1
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3. (8 points) Check all the boxes which correctly characterize each function, leaving the other boxes blank. (ALTERNATES: see end.) f : N N such that f ( n ) = 3 n 3 + 7( n 2 n ) O ( n 3 ):
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