Hw3-sol - CS 173 Discrete Structures Fall 2011 Homework 3 Solution This homework contains 4 problems worth a total of 40 points It is due on Friday

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, Fall 2011 Homework 3 - Solution This homework contains 4 problems worth a total of 40 points. It is due on Friday, September 16th at 4pm. When writing your proofs, be sure to use the definitions of key concepts (e.g. divisible) as presented in class. Also one goal of this problem set is to practice certain proof techniques. So be sure to use the proof technique specified by the problem instructions, even if there might be other ways to prove the claim. 1. Proof by cases [8 points] Problem 5 from Homework 2 defined the “extended real numbers.” An extended real number has the form a + bǫ , where ǫ is a special new positive number whose square is zero. To compare the size of two extended real numbers, we use the definition: a + bǫ < c + dǫ whenever either a < c , or a = c and b < d . Using this definition and proof by cases, prove the following claim: Claim: For any extended real numbers a + bǫ , c + dǫ , and p + qǫ , if a + bǫ < c + dǫ and c + dǫ < p + qǫ , then a + bǫ < p + qǫ . Solution: Suppose that a + bǫ , c + dǫ and p + qǫ are extended real numbers such that a + bǫ < c + dǫ and c + dǫ < p + qǫ ....
View Full Document

This note was uploaded on 09/19/2011 for the course CS cs173 taught by Professor Fleck during the Fall '07 term at University of Illinois, Urbana Champaign.

Page1 / 3

Hw3-sol - CS 173 Discrete Structures Fall 2011 Homework 3 Solution This homework contains 4 problems worth a total of 40 points It is due on Friday

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