Relations and Functions: What is a Symmetric Relation?

This short video provides an explanation as to what a Symmetric Relation is, from the topic: Sets, Relations, and Functions.

[marieamiee]

I am drowning in my discrete mathematics class and your videos are saving my life! Reading through the relations unit in my textbook I was completely lost, but you've made the concept so understandable.

[kittyfly]

Best explanations on relations I have found so far in books, lectures, other videos, thank you!

[Brlitzkreig]

By far the best videos on these topics

[motionocean]

I know you made these videos in 2016 but I'm telling you right now, thank you so much. These video will foster the next generations of keen academic students greatly. Thank you so much for making these videos

[johncoates]

Excellent. And wonderfully soothing accent!

[mohamedtarek]

Greetings from Egypt sir. Thanks for the explanation

[dnr]

This channel is getting me through my classes, thanks mate!

[GauravG]

Just needed that only.. cleared my doubt. Thanks great video

[kaushikchandrasekhar]

You are just superb. THanks for the video

[rajendramisir]

Sir, you used a good method and useful examples to teach what is a symmetric relation. I suppose this discussion can be extended to the Cartesian product of two different sets A and B.

[archiebagnes]

Thank you sir, now i know what is symmetric. ❤️😊

[ghost_nut]

The answer u guys are looking for is at 4:23

[harryklomp]

Thank you very much for your videos. You explain things very clearly.

May I please ask you two questions?



1.

Towards the end of this video you provide a "more refined" definition of a symmetric relation in which you state that:

"Given a relation R on a set A, R is symmetric if and only if for each (x, y) E R, we have (y, x) E R."

I might have missed something, but may I ask you: doesn't this second definition omit the crucial requirement that x, y E A (ie, that all elements in A must be represented in the relation R)? Otherwise, the following relation would be symmetric:

A = {1, 2, 3}

R = {(2, 3), (3, 2)}




2.

Do x and y need to be different? For example, is the following relation, as it stands, a symmetric relation (assuming all other criteria are fulfilled)?

R = {(1, 2), (2, 1), (3, 3)}




Thankyou very much for your help.

[abdullahalhrbi]

Here another definition
ِA relation R is Symmetric if whenever (a, b) (- R then (b, a) (- R