Consider the set of integrity levels L = {low, admin, kernel}, where kernel > admin > low. Furthermore consider the set of categories Cat containing Cat = {HRandAdmin(H),MarketTraders(T),IT Engineers(E)}.
Question: Name and compute the following bound in the product lattice: (admin,{E}) ∨ (kernel,{H}).
Answer: LUB, Least Upper Bound, = (kernel,{H,E})
In the above example I completely understand that kernel is the highest level and we combine the categories. However, why do I get a bad feeling that there are slightly harder examples where this simple trick does not apply?
Lastly, how would I calculate the GLB?
I am hoping to avoid maths if possible.
Given two sequences A = (a,b,c), B = (u,v,w) you want to find the least upper bound of (b,w) and (c,u). It is (c,w).
The greatest lower bound is (b,u).
I'd explain more but as you do not want to bother with math, I won't.
Exercise. Prove, given two linear orders A,B,
that for AxB with the product order,
sup{ (a,b), (x,y) } = (sup{a,x}, sup{b,y}),
inf{ (a,b), (x,y) } = (inf{a,x}, inf{b,y}).