The Gateway to Computer Science Excellence
0 votes
110 views
Consider F be a family of all subsets of set {1, 2, 3, ..... 100} that contain atleast 50 numbers, partially ordered with respect to containment. Then maximum size of chains in the Poset (F, ⊆) that cover F is ________.

-------------------------------------------------------------------------------------------------------------------------------

Answer given 51

but why not 100?
in Linear Algebra by Veteran (118k points) | 110 views
0
yes it should be 51

1 Answer

+1 vote
Best answer
An antichain  in a partially ordered set is a set of elements no two of which are comparable to each other, and a chain is a set of elements every two of which are comparable.

A maximum or longest chain is one which is of the greatest size possible. The size of the longest chain is known as a poset’s height.The following gives an example of such a chain

                                                            {1, 2, . . . , 50} ⊂ {1, 2, . . . , 51} ⊂ · · · ⊂ {1, 2, . . . , 100}

which is the maximum size of chain i.e. 51.Hence, the answer is 51.
by Active (1.7k points)
selected by
0
comparable mean?
0
x and y are comparable if x ≤ y and/or y ≤ x hold
0
ok 50 to 100- total 51 subsets
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,741 questions
57,251 answers
198,058 comments
104,685 users