Chain and Antichain - Poset and Lattice - Discrete Mathematics

Subject - Discrete Mathematics
Video Name - Chain and Antichain
Chapter - Poset and Lattice
Faculty - Prof. Farhan Meer
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[@atharva_513]

this sir is teaching as if its a normal diagraph but its a hasse diagram in which elements are related to each other according to its position in diagram. In hasse diagram all the edges are pointed upwards to show its relation with one another. In first example , according to hasse diagram concept , we can traverse from 'a' to 'b' and 'c' but we cannot traverse from 'b' and 'c' to 'a' , similarly we can traverse from 'b' and 'c' to 'd' but we cannot traverse from 'd' to 'b' and 'c'. Therefore the chains and anti chains concept in this example will be:- Chains:-{a,b} ,{a,b,d} (in this a and 'd are also chains as we can traverse from 'a' to 'b' and then from 'b' to 'd') antichains:-{b,c} (in this we can traverse from 'b' to 'd' but we cannot traverse from 'd' to 'c' because in hasse diagram we show relations between elements in upward manner so here 'd' to 'c' is downward traversing that means there is no relation between 'b' to 'c' therefore {b,c} is an antichaun i hoped this cleared some doubts....Plz reply if it did

[@yugsolanki4766]

yess, thanku so much

[@ShubhamMishra-kd8uv]

thank you

[@vivek0600]

As you included (2,4,..) in first two anti-chain example. How they are not related to each other as 2 divides 4.

[@_hrutik.king_]

That's exactly what I was going to comment

[@sypher4735]

Not every element divides each other.

[@harshrajsharma5050]

3 6 9 18 isnt a chain either cuz there is no relation in 6 and 9

[@General468]

@@harshrajsharma5050 or maybe there is a relation between 6 and 9 😏

[@harshrajsharma5050]

@@General468 bas yahi sab karo tum padhai chod kar

[@dhruvilpatel2480]

why 2 and 4 take in antichain

[@SAMEER_99]

Exactly +1

[@mekersemito]

Basically for the hasse diagram you came up you could have write all the chains like {},{a},{b},{c},{d},{a,b},{a,d},{a,c},{b,d},{c,d},{a,b,d},{a,c,d} because each pair in the subset are comparable and for antichain in similar manner...

[@pranavpurkar9141]

Sir , kindly check your examples of antichain i think there are some mistakes in it.

[@khamkarshreyash]

Absolutely mistake

[@xyzw1850]

Please once go through the content(ex. etc.) which you are going to deliver, its my request!

[@zeyedetekalign3829]

Hi Thank you for your presentation. I have a questiin on total ordering or linear... you gave 2,4,8,12 are examples of total ordered elements but 8 and 12 are not related si hiw it could be a member of a part of total ordered

[@purnimaprusty7219]

I also have the same doubt

[@purnimaprusty7219]

I thought ekeeda is a relaible platform..but was wrong

[@Swan-c3l]

That is very interesting. Thank you.

[@mohitshakya0798]

In example c me 8,12 are not related, sab galat padaya h

[@forg_tful6221]

Thank you very much Sir

[@AshishMishra-do6qb]

You have told that a related to d so why b is not related to C??

[@shubhamrathore7694]

6 and 9 do not satisfies the condition for chain as they do not obey the rule of a/b

[@pantsah4]

check the example c

[@gautamkaushik4380]

Sir you are a good teacher but please don't give incorrect examples

[@raghavendrakumarsingh4646]

Nice explantion of the topic

[@mohitshakya0798]

Phle subscribe kar rkha tha , ab unsubscribe kar diya

[@riteshphadtare4211]

Wrong

[@pujakundu2655]

Hasse diagram is wrong ..

[@yamanmishravilogs]

Aapko hindi nahi aati kya??

[@AshishMishra-do6qb]

What the hell are you teaching