RELATIONS - DISCRETE MATHEMATICS

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Looking for paid tutoring or online courses with practice exercises, text lectures, solutions, and exam practice? TrevTutor.com has you covered!
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.

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26 дек 2014

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Комментарии : 357

@Trevtutor 9 лет назад

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 8 лет назад

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 8 лет назад

thanks dude...

@Thegr8Gupta 7 лет назад

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

@ward7576 7 лет назад

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 7 лет назад

So x , y, z are not distinct?

@sontath7102 6 лет назад

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 5 лет назад

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 4 года назад

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

@md123180 4 года назад

@@foxxul My teacher only posts links to RU-vid 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 3 года назад

@@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 2 года назад

Me 2 lol

@richardt.rogers2730 5 лет назад

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

@MuhammadIsmail-un3qd 4 года назад

he explained really well 😏

@MaxzeeKVO 7 лет назад

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

@preciouslauranoriega4831 4 года назад

Sana all

@nichol071 4 года назад

@@preciouslauranoriega4831 ito hinahanap ko eh HAHAHAHAHAHA

@preciouslauranoriega4831 4 года назад

@@nichol071 HAHHAHAHAHA FILIPINNOOOOOOOO

@preciouslauranoriega4831 4 года назад

@@nichol071 HAHAHA troo

@kenzgaming6398 4 года назад

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

@loremipsum5697 6 лет назад

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

@kallychicken7654 2 года назад

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

@561Aloha Год назад

I'm in Com Sci too!

@bassitirfan7446 Год назад

@@561Aloha same

@krizh289 Год назад

@@561Aloha same

@groundg8397 3 года назад

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.

@extremelyhappysimmer 5 лет назад

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

@KillerKeeton Год назад

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

@rorydaines3176 3 года назад

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

@personaincognita2669 2 года назад

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.

@JP-xm3qf 5 лет назад

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

@DrewBrooksPB 6 лет назад

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

@ndumisomaseko9633 Год назад

How's your exams go?

@mariageorge7600 4 года назад

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

@leafslizer2376 4 года назад

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

@Skyrim_Says 2 года назад

true

@anubhabchakrabortybkppathf6819 8 лет назад

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

@jingu127 4 года назад

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

@28Graysonvb 5 лет назад

The diagrams for reflexive symmetric and transitive help SO much.

@sulafafaleh9297 5 лет назад

What about Anti- Symmetric and irreflexive relationships?

@amosmaggy5020 3 года назад

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

@rajeshdansena 6 лет назад

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 :)

@animejacker4218 4 года назад

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

@ekleanthony7997 3 года назад

I love your course, the explanation is powerful..

@MyCyberAcademy 8 лет назад

Excellent video! Thank you!

@WftYT 3 года назад

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.

@kanjiNaem Год назад

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

@djtygre 3 года назад

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

@marvinrichardson2668 8 лет назад

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).

@ikeikeikeikeikeikeikeike 5 лет назад

You my man, are fantastic, please never stop haha

@fatumeshalla5686 2 года назад

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

@jeremyedbert5092 4 года назад

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

@Carrymejane 5 месяцев назад

Aku telat nih 😁

@Paul-P 7 лет назад

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

@lh5573 7 лет назад

That was brilliant! Thank you so much!

@HK-no9wm 6 лет назад

Extremely helpful. Thank you.

@The6thProgrammer 7 лет назад

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 7 лет назад

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.

@juanbecerra5073 6 лет назад

Great video! Helped me cram for my final

@rosesofficialhusband5728 2 года назад

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

@kingstonmocktail7744 4 года назад

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?

@AvarLalo 3 года назад

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?

@Oskar-ps1dr 7 лет назад

What about Irreflexive and antisymetric?

@XXgamemaster 5 лет назад

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 4 года назад

@@XXgamemaster i appreciate that replay, thank you

@divitasharma 3 года назад

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

@jenicawoitowicz8895 6 лет назад

Thanks for the video! Better than my university prof.

@Start-upsandinvestment 6 лет назад

hi dear.

@Carrymejane 5 месяцев назад

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

@diegovasquezrevilla 3 года назад

Great work! Cheers from Spain and Perú

@kk999la 8 лет назад

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?

@vanessamariemanalac3105 3 года назад

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😊

@triscuit5962 4 года назад

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

@mamo987 2 года назад

you and people like organic chem tutor are god sends

@sulafafaleh9297 5 лет назад

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

@nouraaliabuhlega4023 6 лет назад

you r super hero ,, u saved me thanks

@wudayskitchensaffloho6421 6 лет назад

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

@shwetakhadse7522 8 лет назад

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

@siddharthuzumaki6830 3 года назад

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

@wanoyua8630 3 года назад

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?

@harindudilipa1559 4 года назад

Sir this helped a lot thanks a lot❤️

@Kwatch Год назад

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

@Bryanbro 4 месяца назад

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?

@abdullateefidris-jf3ub Год назад

Thanks 👍,I really understood the relations concept

@071aleksandra Год назад

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

@benlewis-jones6719 3 года назад

the first video that is very good on this topic 👍

@theezakjezuyd8221 5 лет назад

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

@moatazahmed2771 7 месяцев назад

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

@hta-bi249 6 лет назад

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 ?

@rudyeilabouni 7 лет назад

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....

@bagochips1208 2 года назад

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

@goodnightvids Год назад

amazing now i finally understand thanks!!!

@binxing3921 3 года назад

Could you tell me what is anti-symmetric? thank u

@stephaniewainaina4150 3 года назад

What if at 2:01 (x,y)is an element of natural numbers iff instead of x is greater than y it is x

@williamcordova7065 4 года назад

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

@andizacalde2068 8 лет назад

what is the part 2 of this?

@benukhanov960 3 года назад

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

@oliverkiptoo335 6 лет назад

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?

@andizacalde2068 8 лет назад

what is the part2 of this?

@MonkoGames 3 года назад

is there a relation that is reflexive and symmetric but not transitive

@azadalmasov5849 5 лет назад

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 4 года назад

Actually not all rel are functions

@farrukhsaif108 2 года назад

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

@keka54321 5 лет назад

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 2 года назад

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.

@sethmuange9207 5 месяцев назад

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

@elkanacapelle5701 6 лет назад

thank you so much really help alot

@nadianoormohamed4432 7 лет назад

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

@edemcudjoe5053 4 месяца назад

9 years and it's still very comprehensive

@bradfin12 2 месяца назад

Wouldn't it be a type error rather than a syntax error? If function expects input int int and receives float int?

@joanneyuen6308 6 лет назад

thanks! it helps a lot :)

@jemand1685 2 года назад

Thank you for the Video

@zeroanims4113 3 года назад

1:16 I'm new in discrete math and I want to ask if it's valid to write "(x, y) ∈ Z"? because Z means integer set so an ordered pair can't be an element of Z, so shouldn't it must be something like "{ (x, y) ∈ G | x ∈ Z and y ∈ Z }"?

@churchillobiakalusi1593 2 месяца назад

I think the answer for the exercise question is false. If X-y ≠ 0, and y-z≠ 0, it’s doesn’t necessarily mean x-z≠0… For example, when X= 2, y = 1, and z = 2, 2-1≠0 (true), and 1-2≠0(true); however, 2-2≠0(false). Therefore, it isn’t transitive.

@knanzeynalov7133 2 года назад

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.

@WaelAjam 2 года назад

11:09 why would check the symmetry, although the relation does not exist?

@archannel8038 4 года назад

If P={2,3,4},Q={4,6} and for elements of P and Q a relation y=2x exists, then what will be the relations?

@SrgntLoveGaming 6 лет назад

So, was x-y =/=0 transitive? I can't seem to find a counterexample, nor your solution in the description or the comments.

@Trevtutor 6 лет назад

Not transitive. If it were, then 1-2 != 0 and 2-1 != 0 implies that 1-1 != 0.

@semitones9106 6 лет назад

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 6 лет назад

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 5 лет назад

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!!

@xsba7 7 месяцев назад

was struggling so harddd thankk youuuuuuu

@BrandonShippy Год назад

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 5 месяцев назад

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

@YGhost_05 Год назад

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

@buensons 5 лет назад

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

@kingneo4186 4 года назад

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

@divyanshigupta1568 3 года назад

Yes

@astraadamskhan1399 8 лет назад

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

@Trevtutor 8 лет назад

+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 ;)