### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Honors Discrete Mathematics MAD 2104

FAU

GPA 3.65

### View Full Document

## 19

## 0

## Popular in Course

## Popular in Mathematics Discrete

This 4 page Class Notes was uploaded by Chaya Botsford II on Monday October 12, 2015. The Class Notes belongs to MAD 2104 at Florida Atlantic University taught by Jorge Viola-Prioli in Fall. Since its upload, it has received 19 views. For similar materials see /class/221637/mad-2104-florida-atlantic-university in Mathematics Discrete at Florida Atlantic University.

## Similar to MAD 2104 at FAU

## Reviews for Honors Discrete Mathematics

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/12/15

5COUNTEREXAMPLE How do we show that a statement is false In order to answer this question we will introduce the quotevil character mentioned in section 2 the counterexample Assume we need to show that a statement of the form quotlfA then Bquot is false A quick look at the truth table of A gt B shows that the only way for this implication to fail is that A be true but B be false In other words we need to nd one instance in which A is true and B is false Equivalently we must present a particular example called counterexample which makes the statement false Consider for instance the following assertion quotIf n is a positive integer then Pn n2 n 11 is a prime number Let us see what happens when we evaluate P at different values of n J Viola Prioli P1 13 P2 17 P3 23 P4 31 P5 41 P6 53 P7 67 P8 83 P9 101 Observe that each ofthe values obtained is a prime number We have not proved the statement yet however because we have not evaluated P at every n as required in the assertion Next we plug n 10 and get P10 121 11 x 11 so P10 is not a prime We have produced a counterexample thus showing that the statement is false To disprove a statement is an alternative way of asking to provide a counterexample A famous conjecture by Fermat claims that for every natural n the number Pn 22 1 is prime The computations show that PO 3 P1 5 P2 17 P3 257 and P4 65537 each of these resulting numbers is prime But is the conjecture true J Viola Prioli Approximately one hundred years after Fermat39s claim Euler 1739 produced a counterexample actually he showed that P5 that is 232 1 equals 641 x 6700417 and so P5 is not a prime number Another instance which we may encounter is to disprove a statement of the form A ltgt B What does a counterexample need to satisfy in such an instance A look at the corresponding truth table shows that A ltgt B is false only when A is true and B is false or when A is false and B is true In other words a counterexample must show that one of the implications fails perhaps both fail but showing that one fails suf ces J Viola Prioli For instance disprove that quota positive integer n is composite if and only if it has two different prime divisors We notice that this is A ltgt B where A a positive number n is composite and B n has two different prime divisors In our case it is clear that B gt A is true However A gt B fails since 9 is composite so A is true but 3 is its only prime divisor so B is false Summing up n9 is a counterexample to the whole statement quota positive integer n is composite if and only if it has two different prime divisors As a consequence the statement is false J Viola Prioli

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.