Made Easy Test Series | Discrete Maths | POSET | Chain length

Question

1. 50
2. 51
3. 52
4. 53

Answer 1

If we refer this diagram, the max chain length, would be 3.

Similarly, the answer I guess should be 50, but key is ‘52’

 

The provided solution

Comments

@Souvik33 there are 51 elements, not 50; if we take the subset then phi is also counted. So, a chain of 51 comes from the given element, and since phi is connected to all the elements it will add an extra length of 1 to the chain. That’s why it's 52.

please feel free to correct me if I'm wrong

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@TusharKumar See in case of 3 elements, we have 0 <= n <= 3, so max path will have {0 length stuffs}, {1 length stuffs}, {2 length stuffs} and {3 length stuffs}. So like we have levels in tree the no of nodes encountered is 4, but max length is 3 (like height of a tree)

Phi is transitively connected not directly to all, refer the simple 3 elements POSET, I think answer should be 50, not sure tough.

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no in case of 3 elements the set contains {a,b,c} only but here set contains {0,1,2,3,4,…..,49,50} so, total 51 elements and its powerset consists of {0length} {1length} {2length} …..till {all 51in one} . Moreover, you may do a mistake in counting 0 as 0length but actually its 1length so, 0length only contains ‘phi’ which is not directly connected with every other element but for the longest chain, we have to consider that phi is connected to all other elements in a single chain because phi is the subset of every set.

so, the answer should be 52.

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Yes sorry you’re right, there are 51 elements, and yep 0 length is phi, my bad.

But then answer should be 51 (Chain length == height of chain == No. of elements in set)

 

 

Correct if I’m wrong plz...