23.3.4. Hasse Diagram for Subset Relationship

Try these first

1. 1.

   Define partial ordering.

   Hint

   Consider the properties of relations.

2. 2.

   What does poset stand for?

   Hint

   Think about how elements are arranged in this context.

3. 3.

   What are the properties of a partial ordering?

   • Reflexivity
   • Symmetry
   • Transitivity
   • Reflexivity
   • Antisymmetry
   • Transitivity
   • Reflexivity
   • Antisymmetry
   • Irreflexivity

   Hint

   Remember the defining features we discussed.

4. 4.

   A Hasse diagram represents relationships in which type of set?

   • True
   • False

   Hint

   Consider the purpose of these diagrams.

5. 5.

   You have the sets A = {1, 2}, B = {2, 3}, and C = {1, 2, 3}. Explore relations between these sets and construct a Hasse diagram.

   Hint

   Take one set at a time and relate it to the others.

6. 6.

   Create a hierarchy of elements based on subset inclusion using the power set of {x, y}. Show your results through both set notation and a Hasse diagram.

   Hint

   Remember to establish levels as you draw your diagram.