23.3.1. Construction of Hasse Diagrams

Try these first

1. 1.

   What does it mean for a relation to be reflexive?

   Hint

   Think about how every number relates to itself.

2. 2.

   Can you provide an example of an antisymmetric relation?

   Hint

   Refer back to our integer examples.

3. 3.

   What does antisymmetry imply in a partial order?

   • If aRb and bRa
   • then a = b
   • If aRb
   • then a < b
   • All elements are comparable

   Hint

   Focus on the nature of mutual relationships.

4. 4.

   True or False: A Hasse diagram must include self-loops for every element.

   • True
   • False

   Hint

   Consider the properties of reflexivity involved in the diagram.

5. 5.

   Given the set {2, 4, 5, 10, 20} and the relation 'divides', construct the Hasse diagram showing all relationships.

   Hint

   Focus on which numbers divide which and build step by step.

6. 6.

   Using the set {then, when, where} create a Hasse diagram reflecting the inclusion of subsets.

   Hint

   Remember that every subset is part of the larger set.