264 views

recategorized | 264 views

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

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

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
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