24.4.2. Steps of the Algorithm

Try these first

1. 1.

   Define a cover in the context of posets.

   Hint

   Think about the direct relationship in a staircase.

2. 2.

   What is a maximal element?

   Hint

   Is there anything above a maximal element in the hierarchy?

3. 3.

   What is the condition for an element y to cover element x?

   • y must be less than x
   • x ≤ y and no element z such that x ≤ z ≤ y
   • y must be equal to x

   Hint

   Remember, it's about the lack of intermediates.

4. 4.

   True or False: An element can be both maximal and minimal.

   • True
   • False

   Hint

   Consider if an element stands alone.

5. 5.

   Construct a Hasse diagram for the following set of relationships: {1, 2, 3, 4} with the relationships 1 < 2, 1 < 3, 2 < 4.

   Hint

   Consider each relationship to lay out the elements.

6. 6.

   Given the tasks A, B, C, and D where A must occur before B and C, and B must occur before D, list a valid topological order.

   Hint

   Start with the task that has no dependencies.