Reflexive, Symmetric, and Transitive Relations on a Set

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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[jacobjackson]

when you haven't studied for an entire year yet you pass the exam with the help of youtube teachers. amazing

[delealli]

My professor spent two hours trying to explain this to my class and you explain it in 6 minutes. Amazing. Thank you.

[princeoppong]

Always trust YouTube if you wanna pass a test

[novelas]

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!

[lucasm]

Just saved me from a fast 50 min lecture where my professor went over it like it was review.

[s.m.mhamny]

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[stargate]

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[ML-ekur]

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[ysanipena]

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[halo_]

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[dhra]

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[lahiruudayanga]

Damn ! The best explanation for set relations without any doubt.Thanks a lot Mr and keep up the good work

[epilepsyawareness]

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.

[rudyj]

Once again I find myself watching your videos for my class, and once again you fail to let me down.

[nishithbaravkar]

this is the best video on the internet about the topic

[kairaramon]

I usually don't write comments but this is very well explained. What a great video!

[noahrubin]

This is such great revision for me. Cheers

[shivanshu]

He is teaching this to college students and here I am, had to study it in class 11 only.😭

[zacnetic]

Thank you for your knowledge Calvin Harris

[brunostudies]

You've explained this with such simplicity! Thank you so, so much!