21.4.3. Part C: Asymmetric Relations

Try these first

1. 1.

   Define an asymmetric relation in your own words.

   Hint

   Think about what happens if both pairs are present.

2. 2.

   Give an example of a symmetric relation.

   Hint

   Think about family relations.

3. 3.

   If (a, b) is in an asymmetric relation, must (b, a) be in it?

   • True
   • False

   Hint

   Recall the definition of asymmetric relations.

4. 4.

   The relation 'is greater than' on real numbers is:

   • Symmetric
   • Asymmetric
   • Neither
   • Both

   Hint

   Think about the implications of higher numbers.

5. 5.

   Given a set of 6 elements, illustrate all possible asymmetric relations.

   Hint

   Sketch multiple relations and observe patterns in relations.

6. 6.

   Design a proof showing the nature of diagonal pairs in asymmetric relations.

   Hint

   Focus on definitions to establish properties.