Relations and Functions: Composition of Relations

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  • เผยแพร่เมื่อ 24 ธ.ค. 2024

ความคิดเห็น • 45

  • @natedostalik3538
    @natedostalik3538 2 ปีที่แล้ว +1

    You are a savior, this made absolutely no sense to me and now I fully understand the relationship

  • @ProtValnus
    @ProtValnus 7 ปีที่แล้ว +16

    You sir are a rock star. you saved semi frustrated South African student from any further hair loss...consider me subbed

  • @Mister_K_De_Tutor
    @Mister_K_De_Tutor 3 ปีที่แล้ว +1

    Thanks a million. 3rd video I've watched now and felt compelled to comment .

  • @zhenghangxin184
    @zhenghangxin184 4 ปีที่แล้ว +2

    great video

  • @dooham1383
    @dooham1383 6 ปีที่แล้ว +5

    Thank you! I wish there were more teachers like you to teach this course!!

  • @loganholmes7946
    @loganholmes7946 3 ปีที่แล้ว +1

    Thank you very much for taking the time to make this video for free! It helped me understand things so much better!

  • @pveentjer
    @pveentjer 4 ปีที่แล้ว +1

    Excellent explanation.

  • @averysnyder4794
    @averysnyder4794 3 ปีที่แล้ว +2

    This was very helpful! thank you!

  • @expansivegymnast1020
    @expansivegymnast1020 3 ปีที่แล้ว +1

    Thanks for the video! This is a much better explanation than the textbook.

  • @malik_msn
    @malik_msn 4 ปีที่แล้ว

    Thanks. What is the difference between R;S and RoS

  • @jonathanshelnutt8625
    @jonathanshelnutt8625 6 ปีที่แล้ว +23

    thanks SO MUCH! I understand composition of relations now thanks to you! This will help me out in discrete structures a LOT!

  • @collin3012
    @collin3012 4 ปีที่แล้ว +5

    Taking Discrete Math 1 at Western Governors University, and all they give you for the course is a textbook (I'm an online student). Let me tell, you, deciphering this concept from text alone, wouldn't have been possible. Thanks for the explanation! It was simple once someone drew it out in front of me.

    • @carolfloyd6906
      @carolfloyd6906 3 ปีที่แล้ว

      Oh same! The text materials for this course have been okay, but when I got to this topic, deciphering how it was written was a nightmare. This made it much easier to understand!

    • @piklad7477
      @piklad7477 3 ปีที่แล้ว

      Same! Another WGU student here XD Was getting a headache from trying to decipher the text. This was a lifesaver.

  • @HoneyHoney-lh6gu
    @HoneyHoney-lh6gu 3 ปีที่แล้ว +2

    Thank you sir

  • @uriel4829
    @uriel4829 3 ปีที่แล้ว

    My lecturer actually had a different definition for a Composition of Relations FYI for other students. In our lecture notes you are actually looking for y ∈ Y such that (x, y ) ∈ R ∧ (y , z) ∈ S. So you would draw the graph starting with the left set, then the right set. There are other definitions!

  • @isaboo98
    @isaboo98 5 ปีที่แล้ว +3

    so well explained!! you just saved my computer science homework! I will keep watching your videos for help! I wish my professors could explain it that good...

    • @MathsAndStats
      @MathsAndStats  5 ปีที่แล้ว

      Hi Natascha. I am glad it helped. Please share. Regards. Jonathan

  • @priyankankumar6406
    @priyankankumar6406 7 ปีที่แล้ว +1

    Thank you very much Sir.
    You made the concept look so easy.
    Please put your SOCIAL MEDIA links in description.

  • @myanmarchipmunk591
    @myanmarchipmunk591 5 ปีที่แล้ว +2

    Its well explained. Thank you.

  • @nengoz
    @nengoz 7 ปีที่แล้ว +1

    superb explanation

  • @heshammuhammad7622
    @heshammuhammad7622 3 ปีที่แล้ว +1

    I SAW IN ALL BOOKS THAT TO PERFPRM R1oS1 WE HAVE TO PERFORM R1 FIRST WHY YOU PERFORMED S1 FIRST???

    • @MathsAndStats
      @MathsAndStats  3 ปีที่แล้ว

      Hi Hesham, Why don't you send on the book reference. For clarity, the notation R1oR2 means 'R1 after R2,' it doesn't mean 'R1 before R2.' Hence you perform R1 after you have done R2, that is you do R2 first.
      Looking forward to reading one of your references to the texts. I will then reply again. Kindest regards. Jonathan.

  • @es8336
    @es8336 4 ปีที่แล้ว

    okay but my books shows that you dont do from right to left, you do it from left to right? I am confused a lil bit :(

    • @MathsAndStats
      @MathsAndStats  4 ปีที่แล้ว

      Hi E.S,
      Send me the name of the book. I will have a quick look. The convention R1oR2 means R1 after R2, meaning you do R2 first then R1. Please send me the book reference. I will get back to you immediately.
      Regards.
      Jonathan

    • @es8336
      @es8336 4 ปีที่แล้ว +1

      @@MathsAndStats Hello, thank you so much for your answer. You are probably the best teacher I have found online so I would like to ask a question which is buzzing my mind. Since composition is a relation, how can we investigate the symmetry or reflexivity of it? For example, when a and b are elements of a set, and x is a relation between them, we say if axb then bxa and if that's true we say it's symmetric. However, in a composition relation, say a and b are two relations defined from set A to A, aob has a solution, it is also a binary operator(is it?) So, how can I say if composition of relation is symmetric? I literally blew my mind thinking about this, I would be really appreciated if you answer. Thank you for your time.

    • @MathsAndStats
      @MathsAndStats  4 ปีที่แล้ว +1

      Hi @@es8336, Thanks for the kind words. I suppose the quick answer is that the relation created from the composition of two relations is not necessarily symmetric.
      Lets consider some cases, for example: Let A = {1, 2, 3, 4} and let R and S be relations on A defined as: R = {(2, 3), (3, 2)}, and S = {(1, 2), (2, 1)}. Clearly R and S are symmetric, but their composite RoS = {(1, 3)} is clearly not symmetric.
      Say we consider, T = {(1, 2), (3, 4)} and U = {(2, 3}, (4,2)}. Clearly T and U are not symmetric, and their composition UoT = {(1,3), (3, 2)} is also not symmetric.
      Say we consider, V = {(1, 2}, (2, 1)} and W = {(2, 3), (3, 4)}, clearly V and W are symmetric, and their composition VoW = {}, the empty set, which is vacuously symmetric.
      Say we consider, X = {(2, 1), (4, 1} and Y = {(1, 2), (3, 4)}. Clearly X and Y are not symmetric, and their composition XoY = {(1, 1), (3, 1)} is not symetric.
      Say we consider, P = {(2, 3), (4, 1)} and Q = {(1, 2), (3, 4)}. Clearly P and Q are not symmetric, but their compisition PoQ = {(1, 3), (3, 1} is symmetric.
      Hopefully, I didn't make any typos, and I hope this helps.
      Regards. Jonathan.

    • @es8336
      @es8336 4 ปีที่แล้ว

      @@MathsAndStats Yes I totally understand. Also, could I use binary matrix notation of a composition to prove or disprove the symmetry ? By the way, thank you for your answer. As a computer engineering major, I know that I need to learn discrete math instead of memorizing it and truly, your channel is really helping me sir. I wish I had professors like you. When I graduate I will also make videos like yours to help who struggle like me.

    • @MathsAndStats
      @MathsAndStats  4 ปีที่แล้ว

      @@es8336 Here is an interesting observation: proofwiki.org/wiki/Composite_Relation_with_Inverse_is_Symmetric
      It states that R inverse after R is symmetric. I hope that helps.
      With respect to examining the binary matrix representation of the relation. Yes, you could inspect the pairs straddling the main diagonal. For example:
      0 0 0 1
      0 0 0 0
      0 0 0 0
      1 0 0 0 is symmetric but
      0 0 0 1
      0 0 0 0
      0 0 0 0
      0 0 0 0 is not symmetric.
      I hope that helps.
      Regards. Jonathan

  • @pblinfo8531
    @pblinfo8531 4 ปีที่แล้ว +1

    Very helpful !

  • @ABDUllAH-of1gt
    @ABDUllAH-of1gt ปีที่แล้ว

    Absolute legend thank you alot mate

  • @leroythomas1774
    @leroythomas1774 7 ปีที่แล้ว +3

    Thanks a lot it was more than informative, you just give me more confidence to sit my exam.

  • @OnlineEducationAcademyZA
    @OnlineEducationAcademyZA ปีที่แล้ว

    Thank you this is what I needed

  • @weebofthesouth4113
    @weebofthesouth4113 3 ปีที่แล้ว

    This helps me so much thank you, good sir!!!!

  • @reggieroyster6463
    @reggieroyster6463 4 ปีที่แล้ว +1

    I never thought that the Lucky Charms guy would be good at math , but in all seriousness thanks for the help

  • @subhasisbhattacherjee5202
    @subhasisbhattacherjee5202 7 ปีที่แล้ว +1

    Thanks Sir

  • @nileriver2313
    @nileriver2313 6 ปีที่แล้ว

    Thank you for your video!

  • @richasingh9062
    @richasingh9062 4 ปีที่แล้ว

    This was really helpful:)

  • @sal191_
    @sal191_ 6 ปีที่แล้ว +1

    2:47

  • @quirkyquester
    @quirkyquester 6 ปีที่แล้ว +2

    Thank you! amazing teaching!

  • @mahira597
    @mahira597 5 ปีที่แล้ว +2

    Thank you so much!! This helped a lot :')

  • @tristanphillipsshadowalker4633
    @tristanphillipsshadowalker4633 7 ปีที่แล้ว +1

    Many Times Thanks !

    • @MathsAndStats
      @MathsAndStats  7 ปีที่แล้ว

      Your welcome. Feel free to subscribe and recommend to friends. Thanks for watching.

  • @chetanshiv4285
    @chetanshiv4285 5 ปีที่แล้ว

    Thankyou video is really very informative again thanks for this video keep making on such videos brother we really like it and you have a quality to teach others which can help us😊😊👍👌💟

  • @ibraheemwahdan5138
    @ibraheemwahdan5138 4 ปีที่แล้ว

    I love you