23.2.2. Properties of Partial Ordering

Try these first

1. 1.

   Define partial ordering.

   Hint

   What are the three properties of a partial order?

2. 2.

   Give an example of a real-life partial ordering.

   Hint

   Think of how you would arrange a list.

3. 3.

   Which property states that every element is related to itself in a partial ordering?

   • Antisymmetry
   • Reflexivity
   • Transitivity

   Hint

   Think about the properties we discussed.

4. 4.

   True or False: In a partial order, all elements are comparable.

   • True
   • False

   Hint

   Recall the difference between partial and total ordering.

5. 5.

   Given a set of integers, describe how you would determine if the 'divides' relation forms a partial ordering.

   Hint

   Recall the key properties.

6. 6.

   Illustrate a Hasse diagram for the subset relation of the set {A, B, C}.

   Hint

   Sketch your diagram step-by-step.