You need to check EVERY spot for reflexivity, symmetry, and transitivity

A key detail regarding relations is that in order to be, say, symmetric it isn't enough that there is ONE loop that goes out and then comes right back. You need EVERY connection out to have a corresponding connection back. Ditto for reflexive and transitive.

My thank you to the student who kindly agreed to have this video posted.

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[anuragmarola]

i have to finish assignments and found your videos so helpful.. hope i can donate smth to you.

[ramyhuber]

Thanks much for clarification of previous video, I was wondering about this watching the video intro to Ref, Sym and Trans relations.

[blackthorn]

The last example was tricky for sure, but it teaches you to think beyond the obvious :) On point explanations on all of your videos and you helped me out with a lot of questions i had, insta subbing to your channel :)

[Jason-eyjy]

I know it's not in your curriculum, but how would you describe anti-symmetry in this context? The one topic I can't wrap my head around in my course, is the only one you haven't taught!

[DiegoMathemagician]

So if there is a graph where you have only a node and has the reflexive property then it has the symmetric property as well because if a path P is from node A to node A, then the reverse path (inv(P)) would be a path from A to A, and since the original node has a path starting in the node to itself that path is also its reverse and thus, the graph (which had only that node) is symmetric? Or does the node need to have another path from the node to itself in order to have the symmetric property?
Thank you for making these videos, I love how you transmit the passion in your entonation

[nekomaru]

Could you teach me the last example? I'm still not sure how the other twos are true. Is it because of vacuously true?