×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

### Create a StudySoup account

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

or

##### By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

## Intro To Abstract Math

by: Vergie Ankunding

14

0

0

# Intro To Abstract Math MA 315

Vergie Ankunding
Purdue University Calumet
GPA 3.93

Peter Turbek

These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

### Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

COURSE
PROF.
Peter Turbek
TYPE
Class Notes
PAGES
0
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 0 page Class Notes was uploaded by Vergie Ankunding on Sunday November 1, 2015. The Class Notes belongs to MA 315 at Purdue University Calumet taught by Peter Turbek in Fall. Since its upload, it has received 14 views. For similar materials see /class/232684/ma-315-purdue-university-calumet in Mathematics (M) at Purdue University Calumet.

×

## Reviews for Intro To Abstract Math

×

×

### What is Karma?

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

Date Created: 11/01/15
MA 3157 Spring 2009 Implications And An Implied For All77 Assume A and B are conditional statements We de ned the truth value of the conditional statement If A then B77 as follows A B A x B Tr ue Tr ue Tr ue True False False False True True False False True In the last class we considered the following conditional statement If n is even7 then 71 is divisible by 3 Applying the truth table to this conditional statement yields n is even 71 is divisible by 3 n is even i n is divisible by 3 True True True True False False False True True False False True We determined integers n which apply to each row of the truth table For example7 1 n 6 yields the values in the rst row 2 n 4 yields the values in the second row 3 n 9 yields the values in the third row 4 n 11 yields the values in the fourth row This yields that the conditional statement7 If n is even7 then 71 is divisible by 3 is true or false depending on the value of 71 On the other hand7 a mathematician would say that the satement If n is even7 then 71 is divisible by 3 is false This is because7 in mathematics7 implications almost always have an implied7 For all in front of them The statement7 For all 717 if n is even7 then 71 is divisible by 3 is a false statement7 because there are values of 717 for example 71 4 for which the statement is not true Consider the statement7 If n is odd7 then 71 1 is even Since there is an implied for all in front of it7 the statement really is7 For all 717 if n is odd7 then n1 is even Notice that7 in deciding the truth of this statement7 the truth table still comes into play7 in fact7 the de nitions it contain allow us to conclude that this is a true statement The for all forces us to consider the case that 71 may be even the truth table allows us to conclude that the implication is true in this case since the hypothesis is false Note that the statement For all 717 if n is even7 then 71 is divisible by 3 is false However7 there are values of 717 for example7 n 6 for which this statement is true This is expressed by the statement There exists an n with the property that n is even and n is divisible by 3 Notice that this statement is not an implication it contains a conjunction of the hypothesis and conclusion If you try to express this idea by using an implication you will probably not obtain the statement you desire For example the statement There exists an n such that if n is even then 71 is divisible by 3 is true if we can nd one integer n that has the property if n is even then 71 is divisible by 3 It is true that n 6 has that property It is also true that n 11 has that property since 71 11 is not even the hypothesis of if n is even then 71 is divisible by 3 is false and so the implication is true in this case MA 3157 Spring 2009 More on sets and logic Exercise Let A7 B7 and C be sets How can you rewrite each of the following sets PI OVS your answers are correct 1 A m B u 0 2 A o B m 0 Exercise Let A and B be subsets of a set D How can you rewrite each of the following sets Prove your answers are correct 1 A U B0 2 A Bc Exercise Assume A and B are integers Assume C is a subset of both A and B Prove or disprove 0 must be a subset of A B We can de ne intersections and unions for more than two sets Suppose I is a set7 and for each 239 E I we can associate a set Ai We de ne UAZ xl 6 Al for some 2396 I ieI Ai 6 Ai for all 2396 I 61 In the above de nitions7 I can be an in nite set Notation Let a and b denote real numbers with a lt b We de ne 1 11 Ma lt z and z lt b 2 119 Ma S x and z lt b 3 ab Ma lt z and x S b 4 11 Ma S x and x S b Exercise Let NJr denote the set of positive integers What are each of the sets equal to Prove your answers are correct 1 1 1 1 0177 7 w 7 39l H Z1 11071 171ll071 Z1mm I01Z 16N 16N 16N 16N

×

×

×

### 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

Jim McGreen Ohio University

#### "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."

Janice Dongeun University of Washington

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

Jim McGreen Ohio University

Forbes

#### "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."

Become an Elite Notetaker and start selling your notes online!
×

### 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.