24.2.2. Minimal Elements

Try these first

1. 1.

   What is a cover in the context of posets?

   Hint

   Think about direct connections in a diagram.

2. 2.

   Give an example of a maximal element.

   Hint

   Look for elements that aren’t related to anything higher.

3. 3.

   What defines a cover in a poset?

   • A direct relation with intermediates
   • A direct relation without intermediates
   • Any relation

   Hint

   Visualize the Hasse diagram.

4. 4.

   True or False: A minimal element in a poset has elements above it.

   • True
   • False

   Hint

   Think about the definition of minimal.

5. 5.

   Create a partially ordered set of at least six elements. Identify all maximal, minimal, greatest, and least elements, explaining each relation.

   Hint

   Define how each element relates to ensure you address all types.

6. 6.

   Using a given set of tasks with dependencies, construct a Hasse diagram and perform a topological sort. Explain your steps.

   Hint

   Focus on dependencies and remember the definition of topological sorting.