23.3.3. Another Example with Divide Relationship

Try these first

1. 1.

   Define partial ordering.

   Hint

   Think about what properties must hold true.

2. 2.

   What does '2 | 4' mean?

   Hint

   Consider the definition of division in integers.

3. 3.

   Which of the following properties defines a partial order?

   • Reflexive
   • Symmetric
   • Transitive
   • Reflexive
   • Antisymmetric
   • Transitive

   Hint

   Think about the definitions of the properties.

4. 4.

   True or False: All elements in a total order are incomparable.

   • True
   • False

   Hint

   Recall the definition of total ordering.

5. 5.

   Consider the integers from 1 to 10. Identify which pairs are comparable using the divide relationship.

   Hint

   Check each integer's ability to divide the other.

6. 6.

   Create a Hasse diagram representing the set {1, 2, 4, 8} under the divide relationship.

   Hint

   Don't forget to follow Hasse diagram simplification rules.