New User Special Price Expires in

Let's log you in.

Sign in with Facebook


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


Create a StudySoup account

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

Sign up with Facebook


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

Already have a StudySoup account? Login here

Discrete Mathematics I

by: Michale Kuhlman

Discrete Mathematics I MATH 125

Michale Kuhlman
GPA 3.85


Almost Ready


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 :)

Preview These Notes for FREE

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

Unlock Preview
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

View Preview

About this Document

Class Notes
25 ?




Popular in Course

Popular in Mathematics (M)

This 1 page Class Notes was uploaded by Michale Kuhlman on Monday September 28, 2015. The Class Notes belongs to MATH 125 at George Mason University taught by Staff in Fall. Since its upload, it has received 18 views. For similar materials see /class/215006/math-125-george-mason-university in Mathematics (M) at George Mason University.

Similar to MATH 125 at Mason

Popular in Mathematics (M)


Reviews for Discrete Mathematics I


Report this Material


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: 09/28/15
Supplementary Lecture NatesfarMath 1251 Alexei V Samsanavich 212007 Lecture 2 Sets Relations and Functions A set S is a collection of distinct objects x1 x2 called elements or members of the set This is written as follows S x1 x2 and the expression x1 6 S says that x1 is a member of S belongs to S The notion of a set does not allow for multiple instances repetitions of the same element in the set while the notion of a sequence an ordered collection does The notion of a set does not relate to the notion of continuity while at the same time it provides a basis for all concepts of continuous data structures which are not a topic here As far as the set theory per se is concerned the nature of elements is irrelevant all that matters is how many elements are and whether two elements x and y are one and the same element x y or not x at y For example a set may contain another set or even itself as its element A set can be empty denoted by Q nite or in nite The number of elements in a set S is called the cardinality of S written as lSl Examples of sets are natural numbers N integers Z rational numbers Q real numbers R complex numbers C A nite set can be de ned by an explicit list of all its elements for example 1 2 3 and 2 are sets However 1 2 2 3 is not a set because the list contains two instances of one and the same element Alternatively a set can be de ned by a formula that speci es its elements for example x x e R x gt 2 LetA and B be two sets They are equal A B iff they contain the same elements or both are empty A is a subset of B contained in B A g B iff every element of A is an element of B In this case B is a superset of A B Q A We say that A is a proper subset ofB A C B or equivalently B is a proper superset ofA B DA iffA g B andA at B Negations are expressed by slashing the corresponding symbols for example e The following is true for any sets A B AgA QgA ABlt gtAgBBgA The set of all subsets of A is called the power set of A denoted PA The unionA U B is the set of all elements that appear in any of the two sets The intersection A n B is the set of all elements that appear in both sets The set di quoterenceAB or AB is the set of those elements of A that are not in B An intuition into these notions is given by the Venn diagram page 44 in the textbook Finally symmetric set difference denoted A or EB is defined as A EB B A U B A n B Cartesian product direct product of sets A and B denoted in this textbook as A X B is de ned as the set of all ordered pairs in each of which the rst element belongs to A and the second element belongs to B These elements are called coordinates of the ordered pair Thus an ordered pair is a sequence of two elements An ordered ntuple is a sequence of n elements If X is a set thenXquot the nth power of X not to be confused with the power set of X is the set of all ordered ntuples overX over X here means composed from elements ofX


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

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

Steve Martinelli UC Los Angeles

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

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!"

Bentley McCaw University of Florida

"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!"

Parker Thompson 500 Startups

"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."

Become an Elite Notetaker and start selling your notes online!

Refund 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


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:

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

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.