Antisymmetric Relations | Discrete Mathematics

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We introduce antisymmetric relations, with definitions, examples, and non-examples. Is a relation being antisymmetric the same as being not symmetric? Can a relation be symmetric and antisymmetric? Can a relation be neither symmetric nor antisymmetric? We answer all these questions. #DiscreteMath
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Опубликовано:

20 июл 2024

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Комментарии : 75

@WrathofMath 2 года назад

Correction: At 1:30, the divides relation should have (2,6) in it.

@swafly 2 года назад

Oh man, I was having the hardest time understanding why some guy was saying that this relation is Antisymmetric. This cleared it up so much! Thank you

@WrathofMath 2 года назад

My pleasure, thanks for watching!

@jingyiwang5113 11 месяцев назад

This is such an amazing video! I have been confused with this point for a really long time. I finally understand it. I am really grateful for your clear explanation!😀

@WrathofMath 11 месяцев назад

So glad to help - thanks for watching!

@Yahya-gb8zn Месяц назад

I have been sitting here for an hour trying to understand this concept, and you just nailed it!

@changggul6663 2 года назад

just found out that this video was posted 3 days ago, and I have exam about this 30 minutes laterr!! YOU HELPED ME A LOT! Thank you!

@WrathofMath 2 года назад

Thanks for watching, so glad I could help! Hope the exam went well!

@changggul6663 2 года назад

@@WrathofMath Just a quick update, I think I passed the exam LMAO just messed up the equivalence classes a little bit >.

@tasnovashahrin5477 7 месяцев назад

Thank youuuu!!!!!!!

@the.graduate 20 дней назад

Another masterpiece!❤ Thanks for answering my basic question, too! I'll be back for more!

@WrathofMath 20 дней назад

Thanks so much! Let me know if you ever have any more questions!

@YuFow Год назад

Fantastic, cleared all of my confusion within the first minute, thank you so much!

@satabd Год назад

Very clear, thank you, It helps my son to understand this subject

@8ARSH8 Год назад

Greeting from Mauritius island...thanks so much for the video man, it really clear things for me😇

@maxwong3903 2 года назад

Ty very much for the help! Really appreciate the work u put in!

@WrathofMath 2 года назад

My pleasure, thanks for watching and let me know if you have any requests!

@mj47_dreamer 5 месяцев назад

Very clear, thank you so much!!!!!

@slasankautube Год назад

Perfect explanation in few second , i have solve all my problems from your single video , thanks lot bro

@WrathofMath Год назад

Glad to hear it - thanks for watching!

@rickgrimes47 Год назад

Holy Maths! This channel is magnificent!

@WrathofMath Год назад

Thank you Pulkit! Let me know if you ever have any questions!

@sourabshaik3741 2 года назад

Finals Tomorrow! your channel is so helpful, thanks a ton!

@WrathofMath 2 года назад

Thanks so much, good luck and let me know if you ever have any questions!

@rahulshendre7089 6 месяцев назад

congrats for 100k subs man

@WrathofMath 6 месяцев назад

Thank you!

@bimbomariano898 Год назад

But sir, in your first example given set A = {1,2,3,4,5,6}, how did (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) become antisymmetric?

@8ARSH8 Год назад

antisymmetric definition: whenever we have (a,b) in set R , we will never have (b,a) in set R ,unless (a=b), so (1,1)(2,2)... can be present.😇

@arimaulanaid Год назад

Thank you for the explaination, now i get that not-symmetric and anti-symmetric is a different thing.

@WrathofMath Год назад

Glad to help!

@user-xh1xr6hl1t 6 месяцев назад

Why two distinct element is never related but still consider symmetry?

@cyanoswag Год назад

Thank you

@user-xm8fz7cv1f 3 месяца назад

you earn one more Subscriber Sir.

@WrathofMath 3 месяца назад

Thank you!

@adrianlowery4764 Год назад

Thank you thank you thank you!

@WrathofMath Год назад

So glad to help - thanks for watching!

@ClamChowderSoup 9 месяцев назад

Thank god for this. I kept having trouble due to the x=y condition. I thought it was something necessary in order for things be antisymmetric. Turns out it’s just there for a disclaimer on reflexive pairs

@WrathofMath 9 месяцев назад

I can totally see how that would be confusing. There are so many different ways a definition can be worded, and some ways are definitely clearer than others. I'm glad this could help!

@vivienshaanika 8 месяцев назад

well explained ..🙌🙌👏

@WrathofMath 8 месяцев назад

Thank you 🙂

@tosiah919 Год назад

At the 5:00 minute mark i dont understand how its antisymetric. Doesnt 1 relate to 1 in the (1,1) . Would it still be antisymetric if you added another (1,1) ( so now its two (1,1)'s ) the same way you added (4,2) to fight the (2,4)

@tosiah919 Год назад

hmm nevermind i think i get it. In the next example at the 7:17 mark you say (a,a)(b,b) is antisymetric and you keep saying keyword: distinct so im guessing it must be two different numbers like how you said (a,b) (b,a) is not antisymetric which explains the (4,2) with (2,4) not being antisymetric . The (a,a) (b,b) explains why with (1,1) being exact same still antisymetirc because they are not distinct from each other

@WrathofMath Год назад

That's correct! For antisymmetry, when aRb and a is not equal to b, bRa must be false.

@yamatanoorochi3149 2 месяца назад

thanks man

@WrathofMath 2 месяца назад

Happy to help!

@twolip2 3 месяца назад

I've heard of another term 'asymmetric'. Whats the difference between antisymmetric and asymmetric? Also, thankyou so much for explanation🙌🙌

@WrathofMath 3 месяца назад

Asymmetric isn't really a common math term as far as I've seen, but it could be used to simply describe a relation which is not symmetric. Any relation with a pair (a,b) but not (b,a) would be an asymmetric relation. On the other hand, antisymmetry requires there is NO pair (a,b) where (b,a) is also in the relation. "Symmetric" requires all symmetries "Asymmetric" requires it not symmetric "Antisymmetric" requires all asymmetries, that is - if a relates to b then b does NOT relate to a.

@twolip2 3 месяца назад

@@WrathofMath got it, thankyou!

@georgelloyd2795 2 года назад

you are still amazing

@shahngofsyg7818 Год назад

Thanks

@WrathofMath Год назад

Glad to help!

@CBanks-ql9xu 2 года назад

Can you make a video on PMI?

@WrathofMath 2 года назад

Thanks for watching and the request! What about PMI do you want? I have plenty of proofs by induction, do you want a proof of the principle using the well-ordering principle? Or just an overview of the principle?

@CBanks-ql9xu 2 года назад

@@WrathofMath an overview of the principles please. Not so much a worked example but how to think through an induction problem. I find myself getting stuck half way through these types of problems