23.2.5. Example with Positive Integers

Try these first

1. 1.

   What does reflexivity mean in a partial ordering?

   Hint

   Think of how you would describe the relationship between a word and itself.

2. 2.

   Provide an example of antisymmetry.

   Hint

   Consider two integers and their divisibility.

3. 3.

   What is one property of partial ordering?

   • Reflexivity
   • Addition
   • Multiplication

   Hint

   Consider the relationship between an element and itself.

4. 4.

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

   • True
   • False

   Hint

   Think about the definition of total ordering.

5. 5.

   Consider a set of numbers {2, 4, 8, 16}. Define the divides relation and create a Hasse diagram.

   Hint

   Start from the smallest factor and build upwards.

6. 6.

   Given the set of subsets S = {A, B, C}, define the subset relation and demonstrate its partial ordering.

   Hint

   Include all possible combinations and conversely related pairs.