17.3.2. Examples of Asymmetric Relations

Try these first

1. 1.

   What is an asymmetric relation? Provide an example.

   Hint

   Think about friendships that are not mutual.

2. 2.

   What does the diagonal in a relation's matrix representation represent?

   Hint

   Visualize how each element relates to itself.

3. 3.

   In an asymmetric relation, if (a, b) is present, which of the following is true?

   • (b
   • a) must be present
   • (b
   • a) may or may not be present
   • (a
   • b) must not be present

   Hint

   Relate it to traffic directions.

4. 4.

   True or False: Every asymmetric relation is also antisymmetric.

   • True
   • False

   Hint

   Think about the 'one-way street' scenario.

5. 5.

   Create three distinct examples of asymmetric relations and justify why each qualifies as such.

   Hint

   Consider combining pairs in your relation.

6. 6.

   Analyze the relationship R = {(1, 2), (2, 3), (3, 1)}; is it asymmetric? Discuss the implications.

   Hint

   Break down each relationship carefully.