For the set X = { 2,3,6,12,24,36}, a relation ≤ is defined as x ≤ y if x divides y. Draw the Hasse diagram for (X,≤) . Answer the following: (i) What are the maximal and minimal elements? (ii) Give one example of chain & antichain. (iii) Is the poset a lattice?
I have tried to solve this question as follows:
R={(2,2),(2,6),(2,12),(2,24),(2,36),(6,6),(6,12),(6,24),(6,36),(12,12),(12,24),(12,36),(24,24),(3,3),(3,6),(3,12),(3,24),(3,36)}
Final hasse diagram:
Maximal Elements:24,36 Minimal Elements: 2,3 Chain={2,6,12,24} antichain={2,3} This poset is not a lattice.
is the answer correct.