### Create a StudySoup account

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

Already have a StudySoup account? Login here

# INTRO TO ABSTRACT MATH MATH 3000

GPA 3.65

### View Full Document

## 30

## 0

## Popular in Course

## Popular in Mathematics (M)

This 1 page Study Guide was uploaded by Cydney Conroy on Thursday October 29, 2015. The Study Guide belongs to MATH 3000 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 30 views. For similar materials see /class/231829/math-3000-university-of-colorado-at-boulder in Mathematics (M) at University of Colorado at Boulder.

## Similar to MATH 3000 at

## Reviews for INTRO TO ABSTRACT MATH

### 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: 10/29/15

Introduction to Abstract Mathematics MATH 3000401 HANDOUT 3 October 24 2007 Review for Exam 2 Practice Problems 1 Prove that for arbitrary sets A and B B is a subset of A if and only if there exists a set X such that A 7 X B 2 Find the number of integers between 1 and 1000 that are divisible by a at least one of the numbers 12 45 50 b at least two of the numbers 12 45 50 c exactly one of the numbers 12 45 50 3 Prove the following statements by induction a 22 8h 7 5 4n2 7 n for all integers n 2 1 b For the Fibonacci sequence f1 f2 f see Exercise 7 on p 69 of the text y is a multiple of 3 for all integers h 2 1 c If 0 lt q lt i then 1 q lt1 2 q for all integers n 21 d If an integer a gt 1 has prime factorization a p111 10 p1 lt p2 lt lt pm are primes and r E N for all i 1 S i S m then the number of positive divisors of a is r1 1r2 1 rm 1 4 a Use the Euclidean Algorithm to nd integers st such that 415 25t 1 b Show that if s t are any other integers such that 415 25t 1 then 251575 and41 t7t 5 Prove that for arbitrary positive integers a and b a there exist integers in and n such that lcmab am and lcma b bn b m and n are uniquely determined and hcfmn 1 6 Prove that the following two conditions on an integer n gt 1 are equivalent 1 n is a prime power that is n pk for some prime p and some h E N ii for arbitrary integers a and b such that ab is a multiple of n either a is a multiple of n or some power b5 s E N of b is a multiple of n 7 TRUE or FALSE Justify your answer a For arbitrary sets A and B A 7 B U B A b There is no odd integer between 2 and 1010 that is the cube of an integer and also the 7th power of an integer c hcfab hcfa ba 7 b for all integers a and b d For arbitrary integers a and b lcma b lbl if and only if hcfa b lat

### 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."

#### "I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"

#### "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!"

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### 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.