Let a = {1,2,3,4,5}, the partial order relation on A. r = {,,,} ∨ IA (1) make the Haas diagram of partial order relation R (2) let B = {1,2,3,4,5} find the maximum, minimum element, maximum, minimum distance, upper bound, infimum, lower bound and infimum of B The second question is {1,2,3,5}. Wrong number

Let a = {1,2,3,4,5}, the partial order relation on A. r = {,,,} ∨ IA (1) make the Haas diagram of partial order relation R (2) let B = {1,2,3,4,5} find the maximum, minimum element, maximum, minimum distance, upper bound, infimum, lower bound and infimum of B The second question is {1,2,3,5}. Wrong number


Remove the ring from the graph of R and destroy the transitivity. The resulting Haas graph is
 
 
The minimum element of B = {1,2,3,5} is 4, the maximum element does not exist, the minimum element is 4, the maximum element is 2,5, the upper bound does not exist, the supremum does not exist, the lower bound is 4, and the infimum is 4