Answer to Question #295543 in Discrete Mathematics for mayank

Question

{1,2,3,4,6,9}find maximal and minimal and least and greatest number

Answer 1

Solution:

Hasse diagram is

• Maximal element is an element of a POSET which is not less than any other element of the POSET. Or we can say that it is an element which is not related to any other element. Top elements of the Hasse Diagram.
• Minimal element is an element of a POSET which is not greater than any other element of the POSET. Or we can say that no other element is related to this element. Bottom elements of the Hasse Diagram.
• Greatest element (if it exists) is the element succeeding all other elements.
• Least element is the element that precedes all other elements.

So, maximal elements are 4, 6, 9.

Minimal element is 1.

Greatest element does not exist since there is no any one element that succeeds all the elements. 

Least element is 1.