CSCI 250 Spring 2012Discrete Structures Archived Class

# Homework 8

## Comments

• Exercises taken from Discrete Mathematics and its Applications, Seventh Edition unless otherwise noted.
• You must show all of your work for each problem!
• Points will be deducted if you do not show all of your work.
• Each problem is generally worth 10 points. Problems with multiple parts may be assigned more points if there are enough parts or each part is significant enough.
• The Review Questions are always related to the section that will be discussed on the assignment due date.

## Details

SectionProblemNotes
1.328Read the paragraph before the problem.
1.444
1.6adf10
1.732Three keys to this problem: First, you need each to be equivalent to the others. This will require 3 or 4 mini-proofs, depending on how you go about it. Second, you do not start all of the mini-proofs by assuming x is rational. Finally, you must use the formal definition of rational throughout your proof.
1.830Make sure you consider every possibility.
36There is in some sense an obvious number to try. That is, given two distinct numbers, there is one number that you can be certain is between them. The trick is then to prove that this number is irrational. If it isn't clear how to do that, what sort of proof comes to mind?
Review Question1On page 186
3On page 186