I had a question in a previous year paper of discrete maths. It asked-
"Determine all the sub-lattices of D30 that contain at least four elements,
D30={1,2,3,5,6,10,15,30}.
"
I came up with the following hasse diagram:
The hasse diagram looks like a cube projected in 2D and from what I understand, every face of this cube should be a valid sublattice with atleast 4 elements, what other sublattices exist with 4 or more elements? And another aside question, is {1,2,3,6} a valid sublattice in this case, because i think it is but the answer key says otherwise. A photo of answer key is also attached. But I think there is something wrong with this answer key altogether because it does not list the whole lattice itself (i.e. all the elements of lattice) as a valid sublattice having greater than 4 elements. I am not good at discrete maths. Any help will be appreciated.
Answer Key:
