GATE CSE
First time here? Checkout the FAQ!
x
+2 votes
121 views

asked in Set Theory & Algebra by Active (1.8k points)  
recategorized by | 121 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 Loyal (4.7k points)  
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 (49.7k points)  
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 (19.3k points)  
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 Loyal (4.1k points)  
Top Users Jan 2017
  1. Debashish Deka

    8608 Points

  2. sudsho

    5398 Points

  3. Habibkhan

    4718 Points

  4. Bikram

    4522 Points

  5. Vijay Thakur

    4468 Points

  6. saurabh rai

    4222 Points

  7. Arjun

    4122 Points

  8. santhoshdevulapally

    3742 Points

  9. Sushant Gokhale

    3576 Points

  10. GateSet

    3394 Points

Monthly Topper: Rs. 500 gift card

19,177 questions
24,073 answers
52,975 comments
20,310 users