GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
223 views
In one text I read that , if n is square free it is DISTRIBUTIVE
in other text I read that if n is square free  it is BOOLEAN ALGEBRA .

Which is most correct ?

Here D36 is not square free then... what conclusion can I make ?
asked in Set Theory & Algebra by Veteran (20.3k points)   | 223 views

We talk about distributivity and boolean algebra only iff it's a lattice(POSET). So, Relation needs to be provided with Set under discussion.

So, the correct question would go like : let $[D_{36},/]$ (or) Set $D_{36}$ on relation divides. (although its know that we talk about division mostly)

4 Answers

0 votes
Dn if n is a square free number,then  it will be a boolean algebra because if it is perfect square ,then its factors will repeat and then it may lead to more than one complement of an element which is actually not a boolean algebra. ...so D36 is not a boolean algebra.
answered by Boss (8.4k points)  
How do you account for distributive ?
0 votes
When we draw the  hasse diagram, 6 doesnt have a complement. Now, for a lattice to be distributive, every element must have unique complement.

Hence, not distributive.
answered by Veteran (15k points)  
0 votes

In Dn ,if n is square free number then it will be a boolean algebra along with the numbe of vertex should be 2^n and number of edges should be 2*2^n-2.

Above is most important condition to identify whether a relation is boolean algebra or not.Above rule is not for distributive lattice.

Distributive lattice fallow the distributive properties and sublattice properties.

Example:: D64 not Boolean algebra but D110 is boolean algebra.

answered by Loyal (4.7k points)  
0 votes
You can simply check whether d36 is distributive  or not by checking whether we can get it by product of distinct primes for example
D30=2.3.5=30 possible  d40=2.2.2.5 not possible as 2 came 3 times not distinct d36=2.3.2.3 not distributive as we did not get it through product of distinct primes
answered by Ajay singh  


Top Users May 2017
  1. akash.dinkar12

    3308 Points

  2. pawan kumarln

    1884 Points

  3. Bikram

    1656 Points

  4. sh!va

    1640 Points

  5. Arjun

    1396 Points

  6. Devshree Dubey

    1272 Points

  7. Debashish Deka

    1162 Points

  8. Angkit

    1048 Points

  9. LeenSharma

    1010 Points

  10. Arunav Khare

    754 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 May 22 - 28
  1. Bikram

    742 Points

  2. pawan kumarln

    510 Points

  3. Arnab Bhadra

    490 Points

  4. bharti

    304 Points

  5. LeenSharma

    248 Points


22,831 questions
29,157 answers
65,233 comments
27,673 users