# hw5 - CS 173: Discrete Structures, Spring 2010 Homework 5...

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CS 173: Discrete Structures, Spring 2010 Homework 5 This homework contains 5 problems worth a total of 50 regular points, plus three bonus points. It is due on Friday, March 5th at 4pm. 1. Functions [8 points] For each of the following functions, give the following information: what is its co- domain? what is its image? is the function onto? is the function one-to-one? (a) f : Z Z such that f ( x ) = 2 x 2 (b) g : N N such that g ( x ) = x ( x +1) 2 (c) h : C R such that h ( ai + b ) = a (where i = 1) (d) k : R 2 − { (0 , 0) } → R 2 such that k ( x, y ) = ( x l ( x,y ) , y l ( x,y ) ) where l ( x, y ) = r x 2 + y 2 2. Nested quantifers [8 points] Prove or disprove each of the following statements (a), (b), and (c). (a) x R , y R , x + y = 0 (b) x R , y R , x + y = 0 (c) x R , y R , x + y = 0 (d) Express the following symbolically. You must not use the ! quanti±er in your solution. For every real number

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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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hw5 - CS 173: Discrete Structures, Spring 2010 Homework 5...

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