23.3. Hasse Diagrams

Try these first

1. 1.

   Define a partial ordering using your own words.

   Hint

   Check the characteristics we discussed.

2. 2.

   Give an example of a partial ordering.

   Hint

   Think of how you would arrange something alphabetically.

3. 3.

   What property ensures that every element relates to itself in a partial ordering?

   • Antisymmetry
   • Reflexivity
   • Transitivity

   Hint

   Think about the basic rules of relations.

4. 4.

   In a Hasse diagram, which edges can be omitted?

   • Self-loops
   • Transitive edges
   • Both A and B

   Hint

   Review how to construct a Hasse diagram to answer.

5. 5.

   Given a set of numbers {1, 2, 3, 4}, determine if the set under the divide relation (|) is a partial ordering.

   Hint

   Check each pair of numbers for divisibility.

6. 6.

   Create a Hasse diagram for the powerset of {X, Y} and explain how you derived it.

   Hint

   Count the total subsets and remember the relationships.