Relations and Functions: What is an Equivalence Relations

This short video presents an overview of what an equivalence relation is, from the topic: Sets, Relations, and Functions.

[@elisabethfesler8878]

Thank you! This helped me greatly.

[@tiutech3994]

I love all your videos, short clear concise explanations.

[@prithadawn5532]

Thanks! And you missed a (2,7) in your relation R1.

[@elvisdjango5920]

Thank you Professor

[@rdmcnew]

Awesome!

[@MathCuriousity]

Hey love you stuff! Question: I’m having trouble understanding what it means for something to be vacuously true. I remember (as a self learner) seeing this during a proof in intro to logic and didn’t understand it there either. Thanks!

[@MathsAndStats]

Hi. Yeah, it is an interesting idea. I'll try to generalise, using words like: something. It basically usually goes something like this: to show that 'something' has some characteristic, you need to typically find an example of that characteristic to convince someone that it exists. Or to show that something don't have a characteristic I need to show that also. So in regard to symmetric relations, for example, well a relation is either symmetric or it is not. To show that it is not you need to convince me by showing me some characteristic that proves that it is not symmetric. With the empty set, for example, you will never be able to find something that convinces me that it is not symmetric. As you would need to give me an ordered pair (a, b) from the set such that the ordered pair (b, a) is not there. But the set is empty. That is what we mean by vacously. I hope that helps. Jonathan

[@MathCuriousity]

@@MathsAndStats thank you for clarifying that for me!! You r the man!! Thanks for your kindness. Love how u write back to your viewers!

[@abdulazizalzamil6872]

Why didn't you use the 9 node in the digraph? . . And thanks for your efforts.

[@MathsAndStats]

Hi Abdulaziz. I could have, but in this example didn't. Well technically we did use it. It has a self loop, just no incoming or outgoing edge to or from another node. Regards. Jonathan.

[@abdulazizalzamil6872]

@@MathsAndStats Oh, so basically its just an example and you could have use it. . Thanks again.

[@kaushikchandrasekhar5401]

missed out a 2,7