23.1. Discrete Mathematics

Try these first

1. 1.

   Define 'partial ordering' in your own words.

   Hint

   Consider what makes it different from a complete order.

2. 2.

   What are the three properties of a partial order?

   Hint

   Use the acronym R.A.T.

3. 3.

   What does a partial order require?

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

   Hint

   Use the acronym R.A.T.

4. 4.

   True or False: In a total ordering, some elements can be incomparable.

   • True
   • False

   Hint

   Reflect on the definition of total ordering.

5. 5.

   Create a new example of a partial ordering using your favorite hobby or interest. Explain the properties it satisfies.

   Hint

   Think about subcategories within a main genre.

6. 6.

   Analyze a scenario where you have 4 tasks in a project: A, B, C, D. If A must precede B, and both B and C must come before D, construct the Hasse diagram and discuss any potential deadlocks.

   Hint

   Visualize task dependencies.