17.4. Antisymmetric Relations

Try these first

1. 1.

   What defines an antisymmetric relation?

   Hint

   Think about the conditions for having both pairs.

2. 2.

   True or False: All diagonal entries in an antisymmetric relation matrix must be 0.

   Hint

   Consider what self-relating pairs would mean in terms of antisymmetry.

3. 3.

   What condition defines an antisymmetric relation?

   • a) Both (a
   • b) and (b
   • a) must be present.
   • b) If (a
   • b) and (b
   • a) are present
   • then a must equal b.
   • c) They may contain any pairs without restrictions.

   Hint

   Think about the implications of having both pairs.

4. 4.

   True or False: An empty relation can be classified as antisymmetric.

   • True
   • False

   Hint

   Consider what absence of pairs implies for the properties.

5. 5.

   Given the relation R = {(1, 1), (2, 2), (1, 2)}, determine if R is antisymmetric and explain your reasoning.

   Hint

   Look for pairs that contradict antisymmetry.

6. 6.

   Create an antisymmetric relation involving the numbers 1 to 4. Provide its matrix and justify your pairs.

   Hint

   Remember to ensure no pairs conflict with the conditions set by antisymmetry.