24.4.1. Definition and Algorithm Overview

Try these first

1. 1.

   Define a poset in your own words.

   Hint

   Remember the properties of the relation.

2. 2.

   What is meant by an element 'covering' another in a poset?

   Hint

   Think about the Hasse diagram.

3. 3.

   What defines a partial order?

   • Antisymmetric
   • reflexive
   • transitive
   • None of the above
   • All elements must be comparable

   Hint

   Recall the three essential properties.

4. 4.

   True or False: A poset can have multiple maximal elements.

   • True
   • False

   Hint

   Think of how elements relate to each other.

5. 5.

   Create a poset with at least five elements having multiple maximal and minimal elements. Describe their relations.

   Hint

   Use a Hasse diagram for clarity.

6. 6.

   Given a set of tasks with specific dependencies, draw out a Hasse diagram and perform topological sorting.

   Hint

   Make sure to respect the dependencies!