17.4.2. Examples of Antisymmetric Relations

Try these first

1. 1.

   Define an antisymmetric relation.

   Hint

   Think about the implication of pairs in a relation.

2. 2.

   Is the relation R = {(1, 2)} antisymmetric?

   Hint

   Look for the reverse pair.

3. 3.

   What defines an antisymmetric relation?

   • If a relates to b and b to a
   • a must equal b
   • If a relates to b
   • then b relates to a
   • None of the above

   Hint

   Think about the implications of pairs being equal.

4. 4.

   Is the relation R = {(1, 1), (1, 2)} antisymmetric?

   • True
   • False

   Hint

   Identify if both pairs exist.

5. 5.

   Define whether R = {(1, 1), (2, 2), (3, 3), (1, 2)} is antisymmetric. Explain your reasoning.

   Hint

   Look for pairs that might contradict.

6. 6.

   Create a set of relations R on {a, b, c} such that R is antisymmetric but contains both (a, b) and (b, a). Can this be done? Discuss why or why not.

   Hint

   Reflect on properties governing antisymmetry.