# Extremal-Elements ```Họ v&agrave; t&ecirc;n: Nguyễn Văn Tuấn
MSSV: 18119208
a) The maximal elements are all values in the Hasse diagram that do not have any
elements above it
Maximal elements= 27,48,60,72
b) The minimal elements are all values in the hasse diagram that do not have any
elements below it
Minimal elements=2,9
c) The greatest element only exists is there is exactly one minimal elements and is
then also equal to that maximal element
Greatest element= Does not exist
d) The least element only exists is there is exactly one minimal element and is then
also equal to that minimal element
Least element = Does not exist
e) the upper boundss of a set are all elements that have a downward path to all
elements in the set
Upper bounds = 18,36,72
f) The least upper bound of a set is upper bound that is less than all other upper
bounds
Least upper bound = 18
g) The lower bounds of a set are all elements that have an upward path to all elements
in the set
Lower bounds= 2,4,6,12
h) The greatest lower bound is the lower bound that is greater than all other upper
bounds
Greatest lower bound = 12
```