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

Honors Discrete Mathematics

by: Chaya Botsford II

Honors Discrete Mathematics MAD 2104

Chaya Botsford II
GPA 3.65

Jorge Viola-Prioli

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

Jorge Viola-Prioli
Class Notes
25 ?




Popular in Course

Popular in Mathematics Discrete

This 6 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 22 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

Popular in Mathematics Discrete


Reviews for Honors Discrete Mathematics


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: 10/12/15
13RELATIONS Given two sets A and B we wish to pair some elements of A with some elements of B in a certain way according to a rule we establish The end result will then be a set of ordered pairs a b with a in A and b in B When a is paired to b we say quota is related to b or that the ordered pair ab satis es the relation A relation R from A to B is any non empty subset of A x B Therefore ab E R indicates that a is related to b We simplify the notation by writing aRb instead which is read quota is related to b through the relation R speci ed in each case J Viola Prioli When AB we refer to quotrelations on A instead of saying quotrelations from A to A Let us see some examples of relations EXAMPLES 1 Let A 1 2 3 B 1 2 4 and de ne R from A to B as follows declare aRb if and only if a lt b 1 Let us list the pairs of the relation to begin with who is related to 1 Only 2 and 4 so we have the pairs 1 2 1 4 Do the same with 2 get 2 2 and 2 4 And with 3 we obtain 3 4 So the pairs are 1 2 1 4 2 2 2 4 3 4 Notice that although 0 4 satis es a lt b1 the pair 0 4 is not in R because 0 i A Notice also that although 1 1E A x B 1 1 R since 1 is not related to 1 J Viola Prioli 2 Consider A 1 2 9 10 and declare a relation in A as follows aRb if a divides b and a t b An easy calculation shows that R 2 42 62 82 10 3 6 3 9 4 8 5 10 Notice for instance that 7 is not related to any number 3 Consider A 1 2 9 10 and declare a relation in A as follows aRb if a divides b g a gt b We see that 1 is related to any number So 1Rb for all b in A Let us consider 2 2R1 because 2gt139 2R2 because 2 divides 2 Likewise 2R4 2R6 2R8 and 2R10 With 3 We have 3R1 3R23R3 3R6 3R9 With 4 4R1 4R2 4R3 4R4 4R8 With 5 5R15R25R35R45R55R10 Likewise 6Rn for all n16 7Rn for all n1 7 8Rn for all n 1 8 9Rn for all n 1 9 10Rn for all n in A It is worth noticing that in this relation we have 4 related to 3 but 3 is not related to 4 J Viola Prioli 4 Let A 1 2 and B 2A Q 1 2 1 2 Notice that A x B consists of pairs with rst component is a number 1 or 2 and second component one ofthe four sets in B Consider the following relation from A to B the pair a X is in R if a is an element of the set X Thus we have 1R1 1R12 2R2 and 2R12 5 Let A and B be as in 4 This time we de ne a relation on B Observe that the pairs are of the form XY with X and Y subsets of 12 We set XRY if x Y Thus RQ 1R1 1R2 12R12 Summing up as you could see in the examples above and also from the very de nition of relation one has ample freedom to de ne a relation Some relations may turn out to be of interest whereas some others might be irrelevant In fact we can easily see how many relations from A to B we can construct They will be many J Viola Prioli So assume A m and B n Therefore IA x B mn Since the number of subsets of A x B is 2 quot and the only subset we can not consider in a relation is the empty set see the de nition of relation we end up with 2mn 1 relations In conclusion of relations from an melement set to an nelement set is 2mn 1 Given a relation from A to B we can de ne a relation from B to A by simply reversing the ordered pairs of R This is called the inverse relation denoted by R39l Of course since R Q A x B we have that R391 Q BxA J Viola Prioli Three of the most important types of relations are the equivalence relations the order relations and the functions We will explore next the rst type J Viola Prioli


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

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."

Jennifer McGill UCSF Med School

"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."

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!"


"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


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.