RELATIONS - DISCRETE MATHEMATICS

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We introduce relations. How to write them, what they are, and properties of relations including reflexivity, symmetry, and transitivity.
#DiscreteMath #Mathematics #Relations
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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.

[@sontath7102]

Thank you. You are literally the only person who can explain this in simple English it seems. My professor seems to get joy from talking in the most confusing, and ambiguous terms possible

[@AZAZA19981907]

It's not always their fault, usually they have limited time and try to provide you with the most accurate statements possible. Though I agree, it's much easier to graps a broader concept after learning the intuition and basic intetion of it on simple examples, i wouldn't be here otherwise :P

[@foxxul]

Try having a teacher who not only does that, but also has a thick Chinese accent.

[@md123180]

@@foxxul My teacher only posts links to KZbin videos...and not Trev or Patrick... I may as well have the lady that designs suits from the Incredibles explaining relations backwards in Dutch while gargling peanut butter. Thank goodness for Google.

[@viewerr69]

@@AZAZA19981907 The problem begins where the college teachers go after completing the syllabus instead of actually teaching. The bigger the difference between the score of best performing student and the worst performing student, the worse the teacher is at his/her job

[@BillboMC]

Me 2 lol

[@Trevtutor]

x-y != 0 This situation is not transitive. xRy and yRz imply xRz. Consider the case 3R4, 4R3, therefore 3R3. We know 3R3 is 0, so the relationship isn't transitive!

[@yeahboi8705]

well if you're given those specific values and are asked if their relationship is transitive you could say yes, but when given only x and y, their relationship must be transitive for ALL values of the given domain, or else its NOT transitive, even if 99.9% of the possible cases are.

[@shawonshurid9218]

thanks dude...

[@Thegr8Gupta]

but if we say this relation for DISTINCT x, y and z, then it is transitive right?

[@ward7576]

Shouldn't it be that z != x to be more understandable in this scenario? 'cause I'm confused af why is it not transitive.

[@rayrutzer7238]

So x , y, z are not distinct?

[@MaxzeeKVO]

I got an A+ on my test.. you're awesome...keep it up 💪👍

[@preciouslauranoriega4831]

Sana all

[@nichol071]

@@preciouslauranoriega4831 ito hinahanap ko eh HAHAHAHAHAHA

[@preciouslauranoriega4831]

@@nichol071 HAHHAHAHAHA FILIPINNOOOOOOOO

[@preciouslauranoriega4831]

@@nichol071 HAHAHA troo

[@kenzgaming6398]

@@preciouslauranoriega4831 pede paturo?? Naguguluhan paren po tlga ako..

[@loremipsum5697]

i wish more teachers were like you. You make stuff way more intuitive and easy to understand.

[@richardt.rogers2730]

"and if you don't get confused... I really hope you don't" haha thank you

[@MuhammadIsmail-un3qd]

he explained really well 😏

[@kallychicken7654]

i just started computer science at uni this year and i got recommended your amazing videos! They are so helpful, even if my main language isnt english i still managed to understand you easily and mathematics have their own universel language which helps even more. Thank you again

[@dianna5619]

I'm in Com Sci too!

[@bassitirfan7446]

@@dianna5619 same

[@krizh289]

@@dianna5619 same

[@groundg8397]

Hey, I just wanna let you know that this video helped me so damn much. Thank you very much, you have no idea how good it felt when I finally had that eureka moment after many weeks having no idea what my professor was talking about. Keep doing what you're doing bro.

[@KillerKeeton]

This is such a better explanation than my professor. Everyone in class struggled with the homework on this topic. This helped a bit

[@JP-xm3qf]

You are an excelent Prof., thank you very much, it was very clever to introduce the logic tables on the symmetric relationship.

[@mariageorge7600]

Your explanation is so easy to understand. Hope our Professors could teach as good as you.

[@rorydaines3176]

I was so stuck on transitive and your less than sign example just exploded a eureka, thanks a million.

[@personaincognita2669]

A correction: every function may also be represented as a relation (i.e., as a subset of a Cartesian product), but not every relation is a function. Just think of a simple relation like a total order on a set and you will see that a given argument in a relation may be related to many other arguments and does not have to be related to an exclusive output as a function does.

[@28Graysonvb]

The diagrams for reflexive symmetric and transitive help SO much.

[@amosmaggy5020]

Thank you for the tutorial...seems like you are the only one who can help me understand what my lec teaches me☺☺

[@DrewBrooksPB]

Glad I found your channel before finals! Wish I found it in August, will recommend! Great stuff, thank you!

[@ndumisomaseko9633]

How's your exams go?

[@leafslizer2376]

0:53 smoothest "L" I've ever seen your handwriting is so satisfying >.>

[@Skyrim_Says]

true

[@extremelyhappysimmer]

11:42 "they want you to play with yourself" oh math, when did you become so enticing?

[@williamcordova7065]

Thank you for putting these tutorials together for all of us that struggle with Math. Very appreciated

[@animejacker4218]

Am really grateful 🙏 your explanation was superb , it really helped me , thanks sooo much , looking forward to more of your videos 😊

[@ekleanthony7997]

I love your course, the explanation is powerful..

[@jingu127]

u save me while I'm studying last minute for my midterm tmr 🤦🏻‍♀️ thank you so much

[@HK-no9wm]

Extremely helpful. Thank you.

[@lh5573]

That was brilliant! Thank you so much!

[@djtygre]

Awesome vid as usual. Thank you for all your help.

[@fatumeshalla5686]

wow , I spend so many hours understanding this but you are awesome !!!

[@MyCyberAcademy]

Excellent video! Thank you!

[@WftYT]

So clear thank you. I don't know why my professor is turned on by using such big words. Your explanation was clear and easy to understand.

[@astraadamskhan1399]

play with your self......:) more teachers should be like this

[@Trevtutor]

+Astra Adams Students who want to play with themselves are encouraged to sit in the back of the room with other students that want to play with themselves, that way they can play with each other instead ;)

[@CharlieJ2588]

I thought I was the only one that caught that xD

[@tF6U]

TheTrevTutor Dawg wtf I was tryna understand discrete math but here you are making sex jokes. Smh math nerds wildin' these days

[@Kevessi]

TheTrevTutor omfg lol

[@jeremyedbert5092]

I'm from Indonesia, and I appreciate this one... Love your explanation

[@Carrymejane]

Aku telat nih 😁

[@ikeikeikeikeikeikeikeike]

You my man, are fantastic, please never stop haha

[@juanbecerra5073]

Great video! Helped me cram for my final

[@Carrymejane]

This is a very good explanation for basic introduction, for one that doesn't learn them at othe sources.

[@jenicawoitowicz8895]

Thanks for the video! Better than my university prof.

[@Start-upsandinvestment]

hi dear.

[@sulafafaleh9297]

Your channel helps me a lot thank you very much 😍😊

[@knanzeynalov7133]

Thank you for the awesome explanatory videos! I have been preparing for my final exams by watching your videos. I hope I will pass the lesson.

[@j.jehml.1446]

it is criminal that a 15 min yt video explains this shit way better than 2 hours of lectures at a uni im paying to go to

[@nouraaliabuhlega4023]

you r super hero ,, u saved me thanks

[@wudayskitchensaffloho6421]

hi i love your videos and requesting if you can make a video on relational closures

[@rajeshdansena]

At 15:05 for proofing it is not transitive you took x and z same. don't you think it's wrong to take same value ? All x,y,z must be of different values? If you still says we can take same values for x and z then in that case, for symmetric property we also can take x and y same and which will say (let) 2=2 and hence it do not hold symmetric property as well. Appreciate you response on my query. Thanks. You are doing awesome job :)

[@abdullateefidris-jf3ub]

Thanks 👍,I really understood the relations concept

[@harindudilipa1559]

Sir this helped a lot thanks a lot❤️

[@siddharthuzumaki6830]

That's nice, You are helping me so much right now.

[@Kwatch]

i like that you use different collor for each section. it makes things much easier to swallow

[@triscuit5962]

About to take a discrete structures test, wish me luck!

[@Paul-P]

the inflection in your voice at 13:20 so excited about math lol.

[@diegovasquezrevilla]

Great work! Cheers from Spain and Perú

[@elkanacapelle5701]

thank you so much really help alot

[@anubhabchakrabortybkppathf6819]

In which video can I learn more about equivalence class and relations?

[@rudyeilabouni]

I'm kinda struggling with this question I have... It's about Hash functions... SHA64 to be specific... It goes like this: We have a set of S which is a random long String combination (Cardinality is infinity therefore) and another set of Hex64, which consists of the Hexadecimals {0,1, 2...., 9, A, B, C, D, E, F) and this function takes any String input and generates a 64 digit long hexadecimal number from that string... However, because there are infinite input possibilities, however limited output possibilities (16^64 to be specific) there are bound to be "collisions" and that is when you enter 2 different strings but get the same output... and now my question is this... The following relationship is defined so: s1 and s2 are elements of S and are related as such: s1~s2 : Hex64(s1) Hex64(s2) So it's basically saying that 2 different strings are related, when they cause a collision and it's saying that this is an equivalence relation, and I have to show: a) How this is reflexive b) how this is symmetric c) how this is transitive Now I understand it in principle, but I'm not sure how to do it mathematically....

[@benlewis-jones6719]

the first video that is very good on this topic 👍

[@sulafafaleh9297]

What about Anti- Symmetric and irreflexive relationships?

[@benukhanov960]

This guy is a fu*king genius. He explained everything so simply.

[@nadianoormohamed4432]

not all relations are functions as implicitly stated in your video. Apart from that great video, thanks.

[@bagochips1208]

god my college discrete math course was so bad that straight up skipping the lecture and only studying the slides and videos like you got me better grades

[@Oskar-ps1dr]

What about Irreflexive and antisymetric?

[@XXgamemaster]

Oskar Midbøe A relation R on a set X is antisymmetric if and only if x R y and y R x implies x = y. A relation is irreflexive if and only if every point x is not related to itself. An example of this is inequality since it’s illogical for an element say x to be not equal itself.

[@mohameddoudou3285]

@@XXgamemaster i appreciate that replay, thank you

[@The6thProgrammer]

When determining reflexivity, symmetry, and transitivity at 11:31. Could we analyze x - y != 0 as x != y instead? Just seems like it may be a simpler approach. Do you see anything wrong w/ that approach? I noticed you actually worked out x != y at the end of the video. My question is: is there anything wrong with manipulating the variables around the operator? I'm assuming this should not change reflexivity, transitivity or symmetry. (i.e. x - y + z = 0 is the same as figuring out the relations of x = y - z, etc.)

[@Trevtutor]

There's nothing wrong with that. In fact, it's easier to understand x != y rather than x-y != 0 for this kind of question, so the fact that you were able to change that and work with it better is a good thing.

[@rosesofficialhusband5728]

I would like to know what app are you using for writing things Trev!

[@philosophyversuslogic]

The last example doesn't work when (xRy, yRz -> xRz) and x=z. For instance, 1-2 doesn't equal 0, 2-1 doesn't equal 0, but 1-1 equals zero.

[@goodnightvids]

amazing now i finally understand thanks!!!

[@azadalmasov5849]

Thank you for your explanations of these kind of intuitive abstract stuff. I heard you saying relations are functions but isn't it vice verse?

[@IStMl]

Actually not all rel are functions

[@farrukhsaif108]

@@IStMl Exactly, but the professor said at the beginning of the video that relations are functions

[@xsba7]

was struggling so harddd thankk youuuuuuu

[@joanneyuen6308]

thanks! it helps a lot :)

[@071aleksandra]

Oh wow! You are a star, keep doing this.

[@mamo987]

you and people like organic chem tutor are god sends

[@edemcudjoe5053]

9 years and it's still very comprehensive

[@alberteinstein983]

hello identity relation is what he explained in the place of reflexive! reflexive relation's are those in which elements are related to themselves, also they can be related to any other element! peace out.

[@divitasharma]

Can u pls tell the software u used here. I found it great

[@javiermelendrez5763]

thank you!

[@shwetakhadse7522]

identity relation is both symmetric and antisymmetric?; can u give more examples for antisymmetric relations?

[@oliverkiptoo335]

A question: Let A = Z the set of integers and let R be define by R b if and only if . is R an equivalence relation?

[@Bryanbro]

In the example x-y=!0, I assume you don't include negative numbers? Because then the relation would not be symmetric right?for example pick x to be -y?

[@kingstonmocktail7744]

So for a set like this {5,10,15,20 ......}, could you say that it follows a relexive relation? Because each element is related to itself?

[@marvinrichardson2668]

Set of all integers where (x,y) is in R. xy>1 is it ref , symm , trans or anti? Could you help me understand more of this? I answered symmetric for this one and I got it correct. e.g (4 2) (2 4) > 1 but what about say (1,0) (0,1)? Also, why can't it be reflexive? like (2,2) but we can't have (1,1) (0,0).

[@jemand1685]

Thank you for the Video

[@castlemagic4746]

11:44 Play with myself? Set Theory doesn't get me quite that excited... Great videos tho man. Thanks.

[@AvarLalo]

Hey, i just wanna know at the end of the video for transitivity, why do we choose x=2, y=1, z=2. What if we choosed x=2, y=1 and z=3, wouldnt that make it transitve?

[@buensons]

0:40 Not all relations are functions....

[@kingneo4186]

Yea! All functions are relations, but not all relations are functions. How could he say this? OMEGALUL

[@divyanshigupta1568]

Yes

[@wanoyua8630]

you made a comment on symmetry: "if the first part is false, then the whole thing is true". Does this logic also apply to the antisymmetric property?

[@urmomispeng1997]

Ily still thanks for the help :)

[@Pandzi]

Thanks fir the help

[@vanessamariemanalac3105]

How do you identify the relation R? Our prof said the condition or formula is x+y divided by 2 and the answer must be an integer. But I am just quite confused bc he gave us a problem to answer but the domain(x) is a vowel and the range(y) is a number. But the formula said that the answer must be an integer to say that xRy. But the set contains vowel and a number, for example (a,2). So my question is can (a,2) be aR2? Hope you can answer my question even after 5 years. Thanks in advance😊

[@oshadayasiru6224]

Thank you, Very usefull

[@Moddapukka]

I just have a question about the less than or equal to operator. Instead of taking the constants 3 and 4 while evaluating the symmetry, what if you were to take two of the same constants, say 4(like you did for the second relation)? The statement would be: =(4 is less than or equal to 4) implies (4 is less than or equal to 4) which is: =(true) implies (true) therefore the overall statement is: =true So my question is why is the operator, less than or equal to, not symmetric? Amazing work btw! Your videos are clear and coherent, keep up the good work!

[@DDRFaQ]

When we pick 4 and 4, we are evaluating one scenario. For a relation to be symmetric it had to be synmetric for all choices of x and y. So yes, (4,4) works, but because we can find a situation where the relation isn't symmetric, we cannot claim that the whole relation is symmetric.

[@Moddapukka]

DDRFaQ Ohhh didn't realise it had to be for all choices for x and y. Thank you for clearing it up!

[@kk999la]

for set like R={(2,3),(3,2), (5,4)} can i say it it symmetric becuz it contains 2,3 3,2...but what i confused is it doesn contain (4,5)..but hv (5,4) ..so it is symetric?

[@theezakjezuyd8221]

On the Transitive relation part, what do you do if you only get 2 variables? i.e. (x > y + 1)

[@moatazahmed2771]

you don't think of it like that, transitive Rel. means if x relates to y and y relates to z, then x relates to z, and it is just a property, i.e. It doesn't enforce that, you check for that, if x relates to z then it is transitive otherwise it isn't

[@michaelkievits7073]

you are great!

[@semitones9106]

Im not really understanding 11:08 you said 4-4!=0 is true because it being false makes it true. Can you clarify this for me some more? Does that only happen in a transitive case and is it like a rule that has to be memorized?

[@needlermasta]

en.wikipedia.org/wiki/Material_conditional#Truth_table Suppose I say: "If I go to the store, I will get eggs." The only time that statement is definitely not true, is when I go to the store and I DON'T get eggs, T -> F. If I don't go to the store, I can't lie.

[@suchithrasuchithra7991]

This is vacuous truth. Implication is false only when the premise holds and the conclusion does not. If the premise is false, the implication is true no matter how absurd the conclusion is!!

[@russelsteapot8991]

So symmetry is like a conditional truth-value, in that if the antecedent is false, then the compound proposition is automatically true.

[@TharanaMayuranga]

thanks a lot

[@MultiGoban]

Thank you

[@sethmuange9207]

I have a question concerning the last equation what if you changed z to 3, wont the equation be transitive

[@keka54321]

In the example when x-y != 0 10:00 It seems as if it's not symmetric, contrary to what is said in the video, because if you pick x as (-3) and y as (3) you get : '(-3) - (3) != 0' imply '(3) - (-3) !=0' which in the second case is false. Have I missunderstood something?

[@twinklerambhia3236]

Both the sides are true , they both are not equal to zero hence by going with the logic truth table of implication the final truth value is true which means it is symmetric for this very example.

[@godsplandrake7392]

for the use of 4 and 4, i thing is not good since 4 is a common viriable so it should be use to check reflexivity not symmetric only......yRx for which mean different

[@hta-bi249]

in the last example where you said it's not transitive but (x not=y and y not = z implies x not =z SO T and T should imply T) so it should be transitive shouldn't it ?

[@Lilybun]

I've watched this video like 5 times now and I still can't get through my course material lol

[@muhammadabdulaziz6489]

lol its nice to not be the only one.

[@prahladsinghrathore6456]

Ok

[@YGhost_05]

We also have something called antisymmetric is it supposed to not be symmetric?

[@annezhang6101]

at 12:25 for the trans part, if x=1, y=0, z=1, then x-z is actually = 0

[@iMunkeez]

for the example x

[@BrandonShippy]

Sorry I am confused still on the symmetric example at 9:15 , is why is it that we don't have arbitrary variables for that example? Could we not prove that it isn't transitive by choosing specific value that would not work in the same manner that we did for symmetric? Thank you for your time!

[@Carrymejane]

Which one u trying to ask? The above or bellow?

[@xkillalex]

You saved my grade ;'D