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# hw5ANSWERS - Neal Whittington(whittin3 Tuesdays at 4:00PM...

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Unformatted text preview: Neal Whittington (whittin3) Tuesdays, at 4:00PM AD9 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 b x 2 c Co-domain: Z Image: { 2 b x 2 c| x ∈ Z } Onto?: No One-to-one?: Yes (b) g : N → N such that g ( x ) = x ( x +1) 2 Co-domain: N Image: { x ( x +1) 2 | x ∈ N } Onto?: No One-to-one?:Yes (c) h : C → R such that h ( ai + b ) = a (where i = √- 1) Co-domain: R Image: R Onto?: Yes One-to-one?: No (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 ) = p x 2 + y 2 Co-domain: R 2 Image: x ∈ [- 1 , 1], y ∈ [- 1 , 1] except ( x,y ) cannot include (0, 0) Onto?: No One-to-one?: Yes 2. Nested quantifiers [8 points] Prove or disprove each of the following statements (a), (b), and (c).Prove or disprove each of the following statements (a), (b), and (c)....
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hw5ANSWERS - Neal Whittington(whittin3 Tuesdays at 4:00PM...

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