17.4.1. Definition and Characteristics

Try these first

1. 1.

   Define an irreflexive relation.

   Hint

   Think about self-connections.

2. 2.

   What is a symmetric relation?

   Hint

   Focus on mutual relationships.

3. 3.

   What defines an irreflexive relation?

   • Every element relates to itself
   • No element relates to itself
   • Only some elements relate to themselves

   Hint

   Consider pairs of the form (a,a).

4. 4.

   True or False: A symmetric relation must have (a,b) and (b,a) for every element.

   • True
   • False

   Hint

   Look at the definition's implications.

5. 5.

   Create a set A and define four different relations on it, identifying which are reflexive, irreflexive, symmetric, antisymmetric, or transitive.

   Hint

   Write down each definition and check if each relation meets the criteria.

6. 6.

   Discuss the implications of having a relation that is both symmetric and antisymmetric. Give an example if possible.

   Hint

   Consider the conditions that must hold for each type of relation.