0 votes 0 votes 50 51 52 53 Graph Theory made-easy-test-series discrete-mathematics + – Souvik33 asked Jan 5, 2023 Souvik33 494 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes 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 Souvik33 answered Jan 5, 2023 Souvik33 comment Share Follow See all 4 Comments See all 4 4 Comments reply TusharKumar commented Jan 5, 2023 reply Follow Share @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 1 votes 1 votes Souvik33 commented Jan 5, 2023 reply Follow Share @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. 0 votes 0 votes TusharKumar commented Jan 5, 2023 reply Follow Share 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. 1 votes 1 votes Souvik33 commented Jan 5, 2023 reply Follow Share 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... 0 votes 0 votes Please log in or register to add a comment.