3 votes 3 votes I am getting 3 minimal please check it Set Theory & Algebra discrete-mathematics set-theory&algebra lattice zeal zeal2019 + – Prince Sindhiya asked Dec 21, 2018 edited Mar 7, 2019 by ajaysoni1924 Prince Sindhiya 869 views answer comment Share Follow See all 11 Comments See all 11 11 Comments reply newdreamz a1-z0 commented Dec 21, 2018 i moved by Lakshman Bhaiya Dec 21, 2018 reply Follow Share It is 3 i also think so. 0 votes 0 votes Magma commented Dec 21, 2018 reply Follow Share I think 'm' and 'n' is only minimal element I know you consider "j" also I have a slightly doubt in it ! 0 votes 0 votes Magma commented Dec 21, 2018 reply Follow Share it can be only 1 minimal element also which is "m" someone clear my doubt in it ! 0 votes 0 votes Prateek Raghuvanshi commented Dec 21, 2018 reply Follow Share @ Magma ,no element is related to some element s ,then s is minimal element .as we can see in diagram element i is not related to anyone else .same thing in m,j also .so total 3 minimal are there. OR we can see like this ,in Hasse diagram all edges has upward direction ,if some element has only out degree that element is minimal element because no element is related to that element 2 votes 2 votes Prince Sindhiya commented Dec 21, 2018 reply Follow Share @prateek bhai i also did it in same way by your first definition but i am not getting this - in Hasse diagram all edges has upward direction ,if some element has only out degree that element is minimal element because no element is related to that element , how to see that which element has outdegree please clear this point 0 votes 0 votes Prateek Raghuvanshi commented Dec 21, 2018 reply Follow Share As you can see except I,j, m all other have in degree also ,only these have out degree only 2 votes 2 votes Magma commented Dec 21, 2018 reply Follow Share thanks you Prateek 1 votes 1 votes Satbir commented Dec 21, 2018 reply Follow Share Put a ball at top most position(say b) and let it roll downwards ....see at what are the possible positions at which it stops (here they could be i,j,m only)....they are the minimal elements. For finding the maximal elements rotate the given Hasse diagram 180 degree and repeat the process. 0 votes 0 votes Prince Sindhiya commented Dec 21, 2018 reply Follow Share thanks PRATEEK BHAI 1 votes 1 votes Mayankprakash commented May 27, 2019 reply Follow Share @Satbir how would you check with same method for 1.maximum and minimum 2.GLB and LUB PLEASE suggest 0 votes 0 votes Satbir commented May 27, 2019 reply Follow Share @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. 1 votes 1 votes Please log in or register to add a comment.
1 votes 1 votes 3 is right. abhishekmehta4u answered Mar 7, 2019 abhishekmehta4u comment Share Follow See all 0 reply Please log in or register to add a comment.