GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
207 views

Identifying a Distributive Lattice

If it is isomorphic to two standard lattice L1* and  L2*  then the lattice is Not Distributive .
If Complemented Then unique complement should exists .

Identifying a complemented Lattice

Atleast one complement exists for every pair of element . (a,b) are complement to each other if meet and loin of (a,b) are Upper Bound and Lower Bound of lattice .

Is My understanding Correct ??

Q1 ]  POSET [{ 1,2,3,6,12}; / ]
         This POSET is a distributive lattice Eventough complement does not exists for 2,3 .
        IF Complement  exists it should be UNIQE. Atmost one complement for every element
       Is my analysis correct ?
Q2]  POSET [{1,2,3}, <= ]

      What is complemet of 1 , 2 and 3 ? Im not able to find out with above understanding
     

asked in Set Theory & Algebra by Loyal (3.2k points) 8 45 88 | 207 views

2 Answers

+3 votes
1. 1 ----> (2, 3) ---> 6 ----> 12, here complement of 12 is 1. For all other elements complement doesn't exist.

2. 1 ---> 2 ---> 3, here complement of 3 is 1 and complement of 2 doesn't exist.
answered by Veteran (48k points) 39 162 393
Thank you sir
basically if a lattice contains L1* or L2*, it is not distributive. Right ??
0 votes

IN Distributive Lattice atmost one complement of each element should be present.

But In complemented lattice at least one complement of each element should be present.

answered by Boss (5.6k points) 3 9 32


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
Top Users Oct 2017
  1. Arjun

    23356 Points

  2. Bikram

    17058 Points

  3. Habibkhan

    8142 Points

  4. srestha

    6254 Points

  5. Debashish Deka

    5438 Points

  6. jothee

    4968 Points

  7. Sachin Mittal 1

    4772 Points

  8. joshi_nitish

    4298 Points

  9. sushmita

    3964 Points

  10. Rishi yadav

    3794 Points


Recent Badges

Popular Question Sonali Rangwani
Notable Question Sandeep Suri
100 Club stdntlfe
Nice Question thor
100 Club Vamp thehacker
Popular Question LavTheRawkstar
Notable Question shubham vashishtha
Nice Answer Habibkhan
Good Question jenny101
Regular Ashish Subscription
27,302 questions
35,156 answers
83,985 comments
33,244 users