Awesome q2a theme
0 votes

Let [N,\leq] is a partial order relation defined on natural numbers. Identify the false statement?

(A). [N,\leq] is distributive but not complemented lattice

(B). [N,\leq] is not a lattice

(C). [N,\leq] is not Boolean lattice

(D). Element 1 doesn't have complement

in Mathematical Logic by (403 points) | 39 views
Is the answer B?

BECAUSE IT IS A LATTICE.(it formas a chain)

But can u tell me what is the definition of boolean lattice?
They mean “Boolean algebra”: A lattice that is both complemented and distributive.

1 Answer

0 votes
  1. Not a lattice
by (1.7k points)
edited by
Can you explain why is it not a lattice? For any two elements we have LUB and GLB right? (The selected elements themselves would be meet and join)
I think He is saying that statement of option $(B)$ is false and hence is the answer too.

$(A)$ given lattice is distributive but it is not a complemented lattice. Because complemented lattice must be bounded and each element must have at least one complement.So, → $True$

$(B)$ this is not a lattice. $\rightarrow False$

$(C)$ This is not a boolean lattice. $\rightarrow True$

       because, In boolean lattice every element has complement. This is not true in given lattice.

$(D)$ $1$ has not a complement. It’s true infact in our lattice no element is having a complement. So $\rightarrow True$

So false statement is $(B)$ and hence answer.
Vimal has the right interpretetion of my sentence..

Gaitonde ko english nehi ata utna a66a..samajh lena bhai..
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
Welcome to GATE CSE Doubts, where you can ask questions and receive answers from other members of the community.
Top Users Jul 2020
  1. Shaik Masthan

    39 Points

  2. hiteshpujari

    9 Points

  3. fazin

    7 Points

  4. srestha

    7 Points

  5. gaurav2697

    6 Points

  6. Venkatesh Akhouri

    6 Points

  7. Meghana518

    6 Points

  8. athenahermes

    6 Points

  9. bittujash

    6 Points

  10. Pawan_k

    6 Points

7,557 questions
1,783 answers
90,491 users