### Create a StudySoup account

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

Already have a StudySoup account? Login here

# Note for MA 101 with Professor LaMaster at IPFW

### View Full Document

## 19

## 0

## Popular in Course

## Popular in Department

This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Indiana University taught by a professor in Fall. Since its upload, it has received 19 views.

## Reviews for Note for MA 101 with Professor LaMaster at IPFW

### 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: 02/06/15

Sets as a Basis for Whole Numbers Revised A set is a collection of objects and the objects are called elements or members of the set The empty set or null set written or Q is the set without any members ie the set of all US states bordering Antarctica is the empty set A nonempty set is finite if it can have its elements listed where the list eventually ends while an infinite set goes on without end ie the set ofintegers 3 2 l 0 l 2 3 is in nite The cardinality of a nite setA written nA is how many members it has What is S if the set S consists of the letters in the word mathematics S m a t h e i c 5 How many members does it has nS 8 Subset of a Set A QB and Proper Subset of a Set A CB SetA is a said to be a subset ofB written A QB if and only if every element ofA is an element ofB SetA is a said to be a proper subset ofB writtenA CB ifA QB and there is an element ofB that is not inA Example The set of the original thirteen colonies is a proper subset of the set of all US states The set of letters in the word math is a proper subset of the set of letters in the word mathematics m a t h C m a t h e i c s CD CS Union of Sets AU B The union of two setsA and B written A U3 is the set of all elements belonging to eitherA or to B or both What letters are in the word math or in the word class The union helps us answer that question IfA m a t h B c 1 a s then A U B m a t h c 1 s Intersection of Sets Am B The intersection of two setsA and B written Am B is the set of all elements common to setsA and B What letters are in the word math and in the word class The intersection helps us answer that question EA m a t h B 0 1 a 5 than A m3 a Two sets are disjoint if they have no elements in common What letters are in the word math and in the word dog Complement of a Set A The complement of a setA writtenA is the set of all elements in the universe that are not inA lfthe universe is the set of the 26 letters of our alphabet the complement of the set of the letters in the word mathematics is the set of the letters of the alphabet not in the word mathematics bdfg Mk lnop qrur wxyz 00 CL 0 Cartesian Product of a Set The Cartesian Product named after Rene Descartes of two setsA and B is the set of ordered pairs which results from matching every element of A with every element of B Example IfA m a t h andB c l a 5 write the Cartesian Product ofA and B Exercises SupposeA 0 1 B 1 2 3 C 0 1 2 Sketch a Venn Diagram to illustrate their relationship Here is one possible Venn diagram A 6 We can resize the circles to show thatA is entirely contained in C and that 2 is a member of both B and C but not inA and 3 is a member only to B So this Venn Diagram is also correct B C Insert the appropriate symbol 6 g C or g in the blank to make a true statement 2 B A B C A U C 2 C A C A A m C 2 e B 2 as C A g B A is not a subset ofB since 0 is inA but 0 is not a member ofB A C C A is a proper subset ofC since all ofA is contained in C and 2 is a member ofC that is not in A C gAUC sinceAUC 0l2 andC0l2 A gA C sinceA C 0landA0l Closure Property for Addition A set of numbers is closed under addition if the sum of any two members including themselves is also in that set A 0 1 B 1 23 C0 12 Which of the sets A B and C are closed under addition NotA ll2 and 2 A Not B 235 and 5 B Not C 123 and 3 C Similarly which are closed under subtraction NotA Oill and 1 A NotB 220 and 0 B Not C 022 and 2 C Which of the sets are closed under multiplication Just set A NotB orC2gtlt 24 and4 B and4 C Which of the sets are closed under division NotA or C l 0 is undefined and in neither set NotB 12 2 and 2 B

### 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

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

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

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "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.