Dark Mode

545 views

3 votes

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.

1