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
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
5166 Points
4204 Points
3748 Points
2986 Points
2298 Points
2234 Points
2142 Points
1998 Points
1626 Points
1552 Points
Gatecse