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.
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!
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!
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...
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.
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
@@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.
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.
@@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.
@@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
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😊😊👍👌💟
You are a savior, this made absolutely no sense to me and now I fully understand the relationship
You sir are a rock star. you saved semi frustrated South African student from any further hair loss...consider me subbed
Thanks a million. 3rd video I've watched now and felt compelled to comment .
great video
Thank you! I wish there were more teachers like you to teach this course!!
Thank you very much for taking the time to make this video for free! It helped me understand things so much better!
Excellent explanation.
This was very helpful! thank you!
Thanks for the video! This is a much better explanation than the textbook.
Thanks. What is the difference between R;S and RoS
thanks SO MUCH! I understand composition of relations now thanks to you! This will help me out in discrete structures a LOT!
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.
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!
Same! Another WGU student here XD Was getting a headache from trying to decipher the text. This was a lifesaver.
Thank you sir
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!
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...
Hi Natascha. I am glad it helped. Please share. Regards. Jonathan
Thank you very much Sir.
You made the concept look so easy.
Please put your SOCIAL MEDIA links in description.
Its well explained. Thank you.
superb explanation
I SAW IN ALL BOOKS THAT TO PERFPRM R1oS1 WE HAVE TO PERFORM R1 FIRST WHY YOU PERFORMED S1 FIRST???
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.
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 :(
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
@@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.
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.
@@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.
@@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
Very helpful !
Absolute legend thank you alot mate
Thanks a lot it was more than informative, you just give me more confidence to sit my exam.
Thank you this is what I needed
This helps me so much thank you, good sir!!!!
I never thought that the Lucky Charms guy would be good at math , but in all seriousness thanks for the help
Thanks Sir
Thank you for your video!
This was really helpful:)
2:47
Thank you! amazing teaching!
Thank you so much!! This helped a lot :')
Many Times Thanks !
Your welcome. Feel free to subscribe and recommend to friends. Thanks for watching.
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😊😊👍👌💟
I love you