Use the algorithm given in the text to find a to-pological sorting for the relation of exercise 16(b) that is different from the “less than or equal to” relation ≤ .

To find:

A topological sorting for the “divides” relation on the set A={2,3,4,6,8,12,18}.

Given information:

A={2,3,4,6,8,12,18}.

Concept used:

Hasse Diagram: It is a mathematical diagram representing a partially ordered set with finite number or members. Involving transitive reduction.

Calculation:

The set has two minimal elements 2 and 3. Either one may be chosen, say pick 3.

The beginning of the total order is

Total order: 3

Set A1=A−{3}, you can indicate this by removing 3 from the Hasse diagram, as shown below. Next, choose a minimal element from A1−{1}. Thus, there are two minimal elements 2 and 5.

Either one may be chosen, pick 5. The total order thus far is

Total order 1≤5

Set A1=A−{1}−{5}=A−{1,5}. You can indicate this by removing 5 from the Hasse diagram as follows.

Next, choose the minimal element from A1−{3}