Reflexive, Symmetric, and Transitive Relations on a Set
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- Опубликовано: 11 сен 2024
- A relation from a set A to itself can be though of as a directed graph. We look at three types of such relations: reflexive, symmetric, and transitive.
A relation is reflexive if every element relates to itself, that is has a little look from itself to itself.
A relation is symmetric if whenever x relates to y, then y relates to x. This looks like every path between x and y has a path back.
A relation is transitive if whenever xRy and yRz, then xRz (this shorthands is read "x relates to y" and so on). This looks like every two step path has a corresponding 1 step path.
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careful, he's a hero
That's ture❤
when you haven't studied for an entire year yet you pass the exam with the help of youtube teachers. amazing
My professor spent two hours trying to explain this to my class and you explain it in 6 minutes. Amazing. Thank you.
Always trust RUclips if you wanna pass a test
My professor is great. I love her lectures and the fact that she knows what she's talking about. However, I missed one and I had to find someone equally as great to teach me. Thanks man!
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@@Aminakzyzz no you
If I have enough resources to visit and thank you, I'd definitely do that man without thanking in comments. The perfect vedio I found so far on youtube to learn relations is this. All three types of relations were came at once and the important part is it was so clear. Thank you for this unconditional help.
Just saved me from a fast 50 min lecture where my professor went over it like it was review.
Holy shit are you me?
Oh yeah...
The sound of the pen kills me slowly
That sound of the pen gives me pleasure. BUT SERIOUSLY! Thank you for these videos!
better than indian accent videos tho
When people said 'math will end you' i didnt actually imagine it to be from a screeching pen
Perit Jan Aydemir I like it. It’s like some sort of ASMR
I came to type this. loool
you are clutching up and you have no idea! Professor was straight yapping for an hour and 15 minutes and in 5 minutes you just explained it perfectly!
Dr. Trefor Bazett, you are honestly my professor right now since my Discrete Math professor does not explain anything at all and does not even want to solve any questions that I might have. Thank you for your video you have clarified all my questions.
Thank you! I'm sorry you've been struggling with your actual professor, but glad I could help a bit:)
Incredibly concise and clear. Thank you!
I know this video is old but man this guy did a great job. Its literally perfect, short to the point with a well articulated explanation and visuals to pair. love it thank you!!!
For anyone interested in Category Theory as a foundation of Mathematics, this is an excellent video to use as a springboard. Prof. Trev would add a letter on the lines (like f or g) to represent the function that makes the line symmetric. Of course symmetric would be more commonly known as a function and its inverse.
Category Theory is so abstract and generalized, that it includes Set Theory within it!
If you understand that last sentence, then you would understand how profound that it is and you should look into some Cat. Theory.
I can't thank you enough! You're out here saving my grades and I'm so glad i found your channel! :))
You are most welcome!
Damn ! The best explanation for set relations without any doubt.Thanks a lot Mr and keep up the good work
this is the best video on the internet about the topic
so much better than my lecturer
I usually don't write comments but this is very well explained. What a great video!
Once again I find myself watching your videos for my class, and once again you fail to let me down.
This is such great revision for me. Cheers
Yes sir! You’ve saved a soul from Zimbabwe 🇿🇼
Thanks but at 5:54 you said "You can go directly from x to y". Shouldn't it be x to z?
He is teaching this to college students and here I am, had to study it in class 11 only.😭
Esa hi hota h
me too this is in ncert class 11
I find these videos very very helpful. I cannot thank enough.
Glad you like them!
You've explained this with such simplicity! Thank you so, so much!
JESUS THANK YOU!!! Why are math professors so stupid to explain something so simple??? You saved the day. STOP DESTROYING THE BEAUTY OF MATH!!!
Exam is in just over an hour. Ur saving me rn fam
Thank you for your knowledge Calvin Harris
Why didn't I find you earlier?! Great clear explanations.
Well done professor , I really like your calm voice
ten outta ten, would come again 💯💯💯
big thanks for you, you've helped me with transitive as well
Thank you for the video! I had trouble understanding this concept until this video
Damn...!! Straight to the point.
Wow, what an amazing video. Thank you so much. Very helpful!
Glad it was helpful!
Thanks mate! You've helped me a ton this semester. My discrete final is tomorrow! Wish me luck!
a year later, how did you do?
I did fine. B+. This channel helped a lot. @@user-dq8yj5qg4r
why i find this guy right now your explanation is just awsome
Thank you, understood it first time
Have been trying to grasp this concept for the longest of time...finally all of it makes sense..thanks😁
Outstanding quality of explanation
the entire class didnt understand the lecturers explanation and he asked us to change our course lol,thanks for the clear explanation
mt profs notes are so confusing on this concept, thanks a lot for the clarity!!
Thank you for the lesson!
You’re most welcome!
If the videos... He post will be of 2 to 3 mins.. He will hit many likes and the concept will be to clear...
Yep... I admit... Hey same surname...coincidence 😆
today I learned I'm not necessarily related to myself? feeling a little reflexive about it.
Oh man you just made this click. I have read my textbook I have watched other videos and nothing made this click until I watched your video.
You just earned a fan from India! 🤙
@@DrTrefor I feel like your channel is very underrated! I checked your channel and you've got some good stuff brother!
Simple and clear
Thank you. This was extremely helpful. It would have been even better if you included antisymmetric as well.
You are the best! Great teaching skills... you make it approachable and intuitive.
This helped me so much ! thank you sir.
Today is my Exam I don't have any idea about that relation but then I found this video now I'm unstopable
Absolutely brilliant
From Bangladesh
Amazing explanation! I loved it!! Thank you Mr. Bazett. ☺
If a relation is reflexive, symmetric and transitive then its called an equivalence relation.
Short and concise! Thank you!
4:27 I might be in the wrong but he said that is does not matter that point z is not involved in this symmetric directed graph for the relation to be symmetric, however the defintion states for all x,y in A, thus indicating that is must be true for all pairs of elements in A. Idk if I understand something wrong here
Not all relations are morphisms. While drawing arrows is good practice- Heoff diagrams / Directed Graphs dont capture the bigger picture
(currently looking for a video that captures the bigger picture)
Excellent explanation. I just wish along with the introduction of these relations we were also given a preview of how they will be useful in the future. You definitely explained it well, but it's still just coordinate gymnastics to me, and I would grasp it intuitively if I only knew the point of it and how these relations will be useful in the future.
Is it necessary that it can go in just 1 step instead of 2 in order for it to be transitive, or 2 is also ok?
Thanks! Such a great explainer!
Fantastic explanation
Ty you just saved my day!
Amazing explanation, straight to the point.
In Transitive, when we have X->Y and Y-> X, should we have X->X and Y->Y too?
I think the answer is yes. I thought the same question while watching as I was trying to find other 2 step paths, which is probably why you asked this. Trefor's statement is correct but unrelated i think
the way u explain is awesome
thankyou for the video. It helps me understand the topic relation.
Yoo! Thanks bro. A lot informative video just over the concept which is the way i like to study.
I have a disorder of listening sharp sound by scratching........ this video kills me, but I have to watch it....
This made me easily understand the topic thank u so much
You are really good
One thing I can't wrap my head around: anti-symmetry. How would you describe that one? Thanks for the video! You've said in 6 minutes what take some, 2 hours to explain.
Thanks man! You're so easy to understand.
directly from my x to my ' says y maps to z'.
Maybe the ASMR will help me remember this stuff for an exam.
Amazing
Is this where graphs (graph theory) come from? Every time we see a directed or undirected graph, is it safe to assume that there is some relation on a set that relates the vertices to each other?
Thank you sir
Seriously a great explanation...!!
I m a 2nd year student nd was confused with these there relations bt sir ur explanation was great.... it was like my own teacher was explaining to me😊😊
Thank you! I had a question(related to this topic) that I needed help with. Is there a way i can reach out to you ?
Thank you sir!
Really helpful.
Suppose we have a set A={ 0,1,2,3} and a R={(0,1),(2,3)} . Is this transitive Sir?
What if there was no path to Z in the last example? Would that relation still be transitive since Z has no relation to the set? (*ie. it is isolated)
thank you
You should start a patreon so you could get in to more specific examples for all of these concepts.
@@DrTrefor I will be your first supporter!
非常簡單易懂,我的離散有救了
Amazingly Described !!
seems "3 different points" has omitted some cases, how about xRy and yRx, but x not R x, is it transitive?
Nope. The x,y,z are just place holders so in your example z was replaced with x, and thus not transitive.
extremely helpful, thankyou!
thank you so much! excellent explanation
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Thank you very much!
GREAT EXPLANATION
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Well explained! Thank you very much, Sir! ^_^ I subbed!