hw5-soln - CS 173: Discrete Structures, Spring 2010...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CS 173: Discrete Structures, Spring 2010 Homework 5 Solutions 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 Solution: Codomain : Z Image : { n Z : n = 2 m for some m Z } , i.e., the even integers One-to-one ? No. For instance, f (0) = 0 = f (1). Onto ? No. The codomain is Z , but no odd integers are in the image of f. (b) g : N N such that g ( x ) = x ( x +1) 2 Solution: Codomain : N Image : { , 1 , 3 , 6 , 10 , 15 , 21 , . . . } Notice that the difference between sequential numbers in this list increases by one as you read from left to right. One-to-one ? Yes. Notice that the sequence is strictly increasing. Onto ? No. For instance, 2 is not in the image of g . (c) h : C R such that h ( ai + b ) = a (where i = - 1) Solution: Codomain : R Image : R One-to-one ? No. For instance, h (2 i + 1) = 2 = h (2 i + 2). Onto ? Yes, since the image and codomain are equal. (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 Solution: Codomain : R 2 Image : The unit circle, S 1 = { ( a, b ) R 2 : a 2 + b 2 = 1 } ....
View Full Document

This note was uploaded on 09/21/2011 for the course CS 173 taught by Professor Erickson during the Spring '08 term at University of Illinois, Urbana Champaign.

Page1 / 4

hw5-soln - CS 173: Discrete Structures, Spring 2010...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online