Yes you are right
Could someone help with this problem?
Determine which of the following posets (S, <=) are lattices.
1. A = {1, 3, 6, 9, 12} and <= is the divisibility relation.
2. B = {1, 2, 3, 4, 5} and <= is the divisibility relation.
3. C = {1, 5, 25, 100} and <= is the divisibility relation.
4. Both 1 and 3
My answer: 3
Is this right? I think it is but I'm not 100% sure.
for divisibility posets, meet is a gcd, and join is a lcm.
#1) 6 and 9 have no join (6 divides 12 but 9 does not)
#2) 2 and 3 have no join, neither do 2 and 5, 3 and 4, or 4 and 5.
#3) is a linear order, that is for all a,b in P: {a∧b,a∨b} = {a,b}. this is not only a lattice, but a complete, distributive one.