in Set Theory & Algebra edited by
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3 votes
3 votes

I am getting 3 minimal please check it 

in Set Theory & Algebra edited by
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4 Comments

thanks PRATEEK BHAI
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1

@Satbir 

how would you check with same method for 1.maximum and minimum

2.GLB and LUB

PLEASE suggest 

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@Mayankprakash

find the minimal i.e. i,j,m then see the diagram again which element is at the lowest level among i,j and m ?

its m ,...so m is the minimum element.

rotate the daigram by 180 and repeat the above step to get the maximum element.

NOTE :- if there are 2 or more elemenet at the lowest level then neither of them will be maximum or minimum element because there can be only 1 maximum and 1 minimum element in a poset.


GLB(meet) and LUB(join) are done wrt to a subset of the poset.

Suppose we take the set {g,h} and then calculate the Join and meet for it.

Put a ball at g and another at h and let them roll downwards. what are the points at which they meet ?

j and m

where they will meet early at j or at m ?  j right ? so j will be meet.

Flip the daigram and do it for getting join

we will get a,d,e,b. but where are they meeting early ?

at d or at e so there is not a join possible

NOTE:- there is only 1 meet and 1 join for a given subset of the poset.

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1 Answer

1 vote
1 vote

3 is right.

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