First time here? Checkout the FAQ!
+2 votes

asked in Set Theory & Algebra by Active (2.3k points) 7 23 62
recategorized by | 264 views

4 Answers

+3 votes

Option a

As complement

m∨n=1 and m∧n=0

m∨p=1 and m∧p=0

So both n and p are complements of m

For distirbutive lattice

N∧(m∨p)= (N∧m)∨(N∧p)

From lhs.    n∧(m∨p)=n∧1=n

From rhs. n∧m=0     n∧p=p

And     0∨p= p

So lhs≠ rhs that's why given lattice is non-distributive

answered by Boss (7.6k points) 46 139 218
edited by
+1 vote
Answer will be (A)

S1: is true because complement of a lattice and lattice has a lub and a glb

S2: Distributive lattice each element has atmost one complement. but here m has 2 complement
answered by Veteran (65.1k points) 35 222 625
0 votes

S1: for lattice to be complemented there should exist LUB and GLB for pair of elements 
eg :(m,n) its LUB is 1 and its GLB is 0
 S2: for a lattice to be distributive complement should be unique in above diagram we have two complements of m that is n,p
so it is not distributive lattice 
so  (A) option 

answered by Veteran (21.4k points) 30 103 201
0 votes
By above diagram you can see that complement of m is n and p.

Since there exist an vertex m such that it have more than on complement so it voilet the deffinition of distributive lattice.
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

    23398 Points

  2. Bikram

    17078 Points

  3. Habibkhan

    8264 Points

  4. srestha

    6296 Points

  5. Debashish Deka

    5438 Points

  6. jothee

    4978 Points

  7. Sachin Mittal 1

    4772 Points

  8. joshi_nitish

    4348 Points

  9. sushmita

    3964 Points

  10. Rishi yadav

    3804 Points

Recent Badges

Notable Question KISHALAY DAS
Notable Question sh!va
Notable Question abhijeetbzu
Great Question jothee
Popular Question rahul sharma 5
Nice Question mohit kumar 5
Notable Question rishu_darkshadow
Nice Comment Pranay Datta 1
Copy Editor Shivansh Gupta
Nice Comment KULDEEP SINGH 2
27,324 questions
35,176 answers
33,279 users