23.2.4. General Definition of Partial Ordering

Try these first

1. 1.

   What does reflexive mean in partial ordering?

   Hint

   Think about how words relate to themselves.

2. 2.

   Is the divides relationship a total order?

   Hint

   Consider if every number can be divided by another.

3. 3.

   What property indicates that each element relates to itself?

   • Transitive
   • Antisymmetric
   • Reflexive

   Hint

   Think about how a word relates to itself in a dictionary.

4. 4.

   True or False: In partial ordering, every element must relate to every other element.

   • True
   • False

   Hint

   Consider the divides relationship example.

5. 5.

   Consider a set of integers from 1 to 10 and define a partial order through multiplicative divisibility. Discuss whether this forms a poset.

   Hint

   Check each property against the definition of poset.

6. 6.

   Construct a Hasse diagram for the set {1, 2, 3, 4, 6, 12} under the divides relation.

   Hint

   Remember to remove unnecessary connections.