@Rupendra Choudhary
If explanation is for +ve integers then no issues but i i have some points to be added if its generelized.
Point a :
About given example set {1,2,3}.
Source : K.H.Rosen
UB or LB may or may not be in a given set.
Point e :
if you consider it for unbounded set then I agree, but may not be valid for every bounded set.
e.g
({ 1,2,3,4,5} , | ) is not a lattice.
point c :
( { 1,2,3,4,6,12,24} , | )
Has elements with more than 1 compliment hence cant be Dist. Lattice.
Please @Pragy Agarwal Sir.