PARTIAL ORDERS - DISCRETE MATHEMATICS

In this video we discuss partial orders and Hasse Diagrams.
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We introduce the concept of asymmetry and partial orders.
Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

[@khaledb8618]

It's 4 am rn, and I have an exam at 10, wish me luck

[@Jessedgnz]

How did it go?

[@navjotsingh2251]

Khaled B first of all, that type of sleeping pattern is damaging to you in the long run please fix this. Second of all, how did you do in the exam?

[@rainbow6siege345]

@@navjotsingh2251 He's dead

[@gmenos6252]

Hope your exams went ok

[@blizzaroxxx]

F

[@Xiorth_YT]

Have my discrete math exam tomorrow morning. Just wanted to say thanks for the videos, they've been great!!

[@atidyshirt]

Have mine this afternoon, this just saved my ass for antisymmetric relations

[@bestyoueverhad.2408]

@@atidyshirt have mine this friday

[@atidyshirt]

@@bestyoueverhad.2408 gl

[@goncalomatias26]

Have mine tomorrow ahaha

[@bassitirfan7446]

so howd u guys do?

[@anonInDE]

You have such a great channel man! I'm studying computer Science and our math prof. does nothing except read out definitions and write them on the board all lecture long... You're really helping me understand what we're actually learning! Cheers man!

[@DanielDupriest]

This is one topic I think I never really figured out from my CS classes. Thank you for the clear and concise explanation!

[@ShanaAngliang]

I like how you mentioned that Hasse Diagrams are used to make relation diagrams clearer, this video has cleared some of my doubts about PO, thank you so much!

[@grigoryshepelev8149]

I've found this video after I had some struggle with understanding "How to prove it" book, which opened a world of beautifull set theory for me. Thank you for those.

[@MrGreyScreen]

You're a better teacher than my lecturer.

[@eduardorivera508]

Thanks for this. Definitely will start binging on these lectures from now on! I love that you explain what each concept means as you introduce them. My professor just mentions them and sort of expects us to know what it means. If it wasn't for this video, I wouldn't have known to have NOT thought of antisymmetry as "not symmetric". No wonder I was confused the entire lecture. Granted, I could have asked out loud, but our class is very quiet. It seems this course is particularly a very intimidating one.

[@ahmedal-tayy7332]

Online Uni is a scam. Im paying 9k this year and all i get is mumbling and a squeaky chair in the recorded lectures. You my man have saved me from failing the maths module in my computer science course.

[@adiletdaniyarov5737]

THe only good discrete math teacher for the whole of the planet

[@adrianalexisoscar1369]

it's easier if you explain transitive inequalities this way 2

[@davidjohnson-my6sr]

3:31: the equivalence class of a is {a,b} by reflexivity.

[@MohammedAlAli]

Thanks Trevor. This is helpful for my Advanced Graph Theory class. We are talking about Comparability Graphs as well as partial order and transitive orientation.

[@GoreDough92]

my dawg Trev killin it on the teaching game, thx bruh

[@user-sf5bt8eb4y]

hey @TheTrevTutor , you are a god send for your discrete math lessons! you are really doing a good thing here, really helpful for students with crappy lecturers

[@JamesBrodski]

Amazing video. Thank you so much. I will pass my exam because of you.

[@tinysosig]

12:46 Trevor you said "We know in a partial order, everything is going to be symmetric", but I think you meant antisymmetric? Correct me if I'm wrong, wanna make sure I'm understanding this correctly.

[@tet5951]

same

[@purpose_is_empty]

He probably actually meant reflexive, because the next step was removing the reflexive arrows.

[@nadeemjq]

This video was exceptionally difficult to follow... Several places it's difficult to see how you're thinking. For example, from 10:40, it's not clear how you are checking for reflexivity. You are merely pointing out the pairs, and not making it clear how that is a check for reflexivity. Anyways, been watching your videos from scratch, and they are lifesavers! :)

[@leocomerford]

0:31 For symmetry, if A has a *particular* relation to B, then we expect B to have *that same* relation to A. If A is related to B then B is *always* related to A in *some* way. If A is the father of B, a very non-symmetric relation, then B is the son of A.

[@marioksoresalhillick299]

2:15, that looks absolutely beautiful!

[@jayantabiswas5689]

sir, if u give more video with example of how to find maximal and minimal number n also for greatest nd least elements ,it will b helpful thax for giving this video

[@TheYagga]

yes please.. great video

[@D.2023]

Clean, perfect explantation. You helped a lot! Thanks!

[@nadeemjq]

Was the conclusion from 11:10 that the set is antisymmetric or not? Not sure what to make of "Yeah, we're looking good here."

[@BusaBarnabas]

At 12:48 you mentioned that, "we know that in a partial order, everything is going to be symmetric..." I am quite sure you meant to say, everything is going to be reflexive.

[@AirTimeEh]

ya i thought a partial order was if R is reflexive, antisymmetric and transitive. staff.scem.uws.edu.au/cgi-bin/cgiwrap/zhuhan/dmath/dm_readall.cgi?page=20

[@evancornish656]

you're right, he made a lot of mistakes in this video.

[@xiaoyulyu]

I was confused at this part, thx

[@stelpveri4679]

Thanks for explaining why the diagram looks the way it does

[@-a5624]

my prof has a link to your channel posted on the online website lol. Your channel is definitely more helpful than his lectures...so thank you :)

[@tallalomar3531]

dude you are the best I have seen so far keep up the good work..

[@martinhawrylkiewicz2025]

Great vid! Just wondering here if you have two partial orders on a set A, will their union be also a partial order on set A?

[@sperera5916]

I have 2 questions. time line 8:29 1. if 2=2 is reflexive, then why x

[@SoBoredTv12321]

Hopefully I can help. x

[@sperera5916]

Thanks alot! I think I got it.

[@mba849]

11:27 how is this relation R symmetric? Its antisymmetric but I don't think it is symmetric since there is no (2,1) or (3,1) which breaks symmetry. Can you please confirm?

[@LuaneCarolineAquinoCavalcanti]

best tutorial about hasse diagrams, thanks !

[@CyberFauxTales]

Perfect, thank you bro.

[@SuegroLM]

I was following up quite well until reached around 11:09 where you explained antisymmetry so vaguely in comparison with the previously explained Reflective and Transitive conditions, from my point of view, I would have liked a better elaboration there, to be honest, 😂 was trying to figure out what was all this about but anyway... before that, I may say it had been a great video.

[@Manikandan-nn2bw]

Perfecto... And thanks for book suggestion.

[@sperera5916]

12:41 Hasse Diagram, you said it is Symmetric, please explain how. Thanks

[@bkevinF]

Hi @TheTrevTutor, thank you for this one. It makes more sense to answer my modules. And also, do you have something that discuss Operations on Relations? Like Complement of a relations, inverse of a relation, composite product, R restricted to X and Image of x under R.

[@cheatcoder2]

Good content, I love it

[@brianc5617]

Love the videos, thanks for doing them! Minor correction: Hasse diagram's are named after Helmut Hasse with Hasse pronounced as hAss-uh

[@adarsh350]

perfect explanation

[@tiku.1414]

+TheTrevTutor So is the "=" relation,an antisymmetric relation,because a=b and b = a implies that a = b.

[@JasonJason210]

Thanks. I find 2:45 onwards confusing. Which is set Y?

[@quocbaoha8373]

thank you Sir, as Vajazle had said, they had been great

[@smoothbrain]

Great vid my guy

[@gazamisehawoh]

thank you this really helped me

[@IndigoStat]

I owe you my life.

[@ahmedhussein660]

Very clearly explained! Thanks a lot.

[@PizzaPunt99]

Very helpful, thanks

[@mimslilas15]

Thank you for your videos! it makes everything look simple :)

[@Trevtutor]

+Marielle Huot Glad I can help :)

[@satyamsinghs786]

I want to know that we delete reflexcivity and transitivity in hasse diagram to make it more clear can i say that 3R1 and 1R2 -->3R2 from hasse diagram since we remove transitivity so i have that doubt plz clear it as soon as possible your lecture are really nice it helped me alot in learning dicrete mathematics thanks for helping us. regards satyam singh IIT BHUBANESWAR INDIA

[@nangalucia7lucia667]

Thank u Sir. Ur video is helpful. Pls make me understand the difference between equivalence class and equivalence relation and also proofs

[@nethajis1384]

How many partial order relations are possible on set of n elements?

[@MRKS8]

thumbs up. Clear and concise.

[@Omer-es7wo]

thank you soo much, all the best for future videos!!!

[@jemand1685]

Thanks for the video

[@jandomingo7162]

I couldn't find Partial Orders in the Book of Proof. Does anyone know if it is actually covered in the book?

[@AnjaliChadha]

Lucid explanation. Thanks!

[@tadiwanashemadongorere2374]

Amazing work!!!

[@Kri38]

thanks for the video man, really appreciate it!

[@irmachan1]

Thank you so much, it really did help.

[@wentaogao2745]

its an irony that youtubers does way better job than mos prof n ta n la that we pay for

[@alialaa8824]

Thank you so much these wonderful videos! I'm having a trouble with reading mathematics notations related to set theory. How can I improve my awareness of reading these notations? I have a course in college that deals with theories of sets and graphs, and I can't understand all the notations especially when it comes to functions and relations that are a bit complex. What do you recommend?

[@orionwolf-hubbard6895]

Thank you! This was very helpful.

[@thunderbeast9831]

I have a question, should we not write "x divides y" as y/x ?

[@andywei8963]

perfect explanations, thanks

[@neuralworknet]

Omg so helpful!

[@utkarshjauhari1443]

Useful topics....

[@novanskaagintaganesha4376]

its very helpful ! thanks sir

[@hibye12345]

You keep saying "we know partial orders are symmetric" but before that you said they are antisymmetric ..... soo which is it?

[@mcsgone4683]

Partial orders are antisymmetric (example: if a

[@snickerdoodle538]

He meant to say reflexive, as he is talking about removing the reflexive edges in the transfer from a graph representation to a Hasse diagram

[@hell4eg]

Thank you for this lessons!

[@Engineer_With_A_Life]

ossum video, now i am cleared with poset but still i confused in symmetric and antisymetric relation both look same :(

[@edgardobaldovinojr.3565]

Hi need some help here, 'cuz im really confused about the antisymmetric property, why is that the relation "greater than" considered as antisymmetric and for this T = {(a,c),(b,d),(d,c)} in relation to X ={a,b,c,d} is considered also antisymmetric . :( please i'm so confused

[@purnimasaikia7776]

Thank u so much , really very helpful !

[@ProphetPakoKadosh]

thanks guys.

[@saladprayer8239]

Thank you so much, man.

[@lobnaabdelhamed1234]

is there any video for closure of relations ?

[@surajmu4169]

You have a video on extremal elements in a poset?? This video was good!

[@ngelemar]

Life saver💯

[@kofiafful7004]

A = {1, 2} and B = {a, b, c}. Is (a, a) an element of A x B?

[@evev6383]

can we draw the hasse diagram horizontally?

[@georghieronymus9935]

Thank you for the informative video. Any prospects for making a video on equivlance classes and partitions?

[@kempisabel9945]

you have saved my exam! TT

[@theone0201]

Thanks mate, you've helped alot :)

[@oumaimaalazhari8704]

Please where can I find the 3rd part of relations, I really need it

[@Kalo953]

I have a question: Why this set if reflexive, by definiton A relation in which all the elements follow the property A→A. All the elements are related to themselves is known as reflexive relation. So if there are ordered couples, which are not reflexive as in the example (1,1) (1,2) (1,3)... then it shouldnt be reflexive?

[@Trevtutor]

+Kalo953 A relation is reflexive, not ordered pairs. If all the pairs of (x,x) are in the relation, then the relation is reflexive. If there are additional pairs, it doesn't change anything.

[@Kalo953]

okay, i understand now, also can i ask why the ordered pairs in the hasse diagram seem to be incomplete. R subset of AxA => AxA = {(1,1),(1,2),(1,3),(1,4)(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1)(4,2),(4,3),(4,4)} ?

[@Trevtutor]

+Kalo953 I don't understand what you mean by "incomplete".

[@Kalo953]

ahh I think i understand it now. You only write the pairs that are related. I thought at first that you write the result of the cartesian product of A^2.

[@Aaztha]

Thank You so much!

[@majidalismaili575]

Which text book are you using?

[@silentrobi2905]

i think it would be like what I see from the book is: [x] ^ [y] != {} cz their are reflexive elements in those set. isn't it, if I am not wrong sir?

[@SmokyBigSmoke]

Thank you

[@TobsterStrudel]

Exam in 4 hours. Here we go lads.

[@purpledorii]

Thank u 🙏

[@dellokrd9916]

Great Vid

[@GoodBalak]

Great Vid! Cheers!

[@deathstalkr_]

For a given poset can we have more than one Hasse diagram?

[@baovoquoc6358]

Thanks, sir.

[@NoraAlfraidi]

When we draw hoss diagram we have to Remove a reflexive sign?

[@hovhadovah]

Note: symmetry does not mean aRb implies bRa, but rather aRb iff bRa

[@Trevtutor]

aRb -> bRa comes out to be that aRb iff bRa. Since 3R2 implies that 2R3 is in the set. But 2R3 in the set implies 3R2 in the set. The simple definition of symmetry is for all a,b, aRb -> bRa.

[@lifehts74]

Awesome 😍😍😍😍

[@amarindersingh8678]

Hey man i have a question. If partial order and total order both are asymmetric, reflexive and transitive then what is the difference between them?

[@manuhortet]

A binary relation is a partial order if it is reflexive, antisymmetric and transitive. But inside partial relations, there are other two types of relations: total order and well-order. What I am saying is that every total ordered set is partially ordered too. The conditions for a partial ordered set to be a totally ordered is that every pair is comparable (xRy is always true)

[@parizer1983]

confused... 9:46 , how can you say that a is a poset with respect to b, when a is an element of the poset called Alphabet and the relation is called "alphabetic order"

[@parizer1983]

he is confusing element of the set and the set it self...learn how to use a comma then call someone dumb

[@SoBoredTv12321]

the poset is the result of the relation of alphabetical order, on the alphabet

[@pushkar9021]

thank you so much .grt work