17.5.1. Definition and Characteristics

Try these first

1. 1.

   Define an irreflexive relation and provide an example.

   Hint

   Consider a simple set with two elements.

2. 2.

   What describes a symmetric relation?

   Hint

   Think about a mirror image in relation.

3. 3.

   What characterizes an irreflexive relation?

   • Self-relation exists
   • No self-relation
   • Some self-relations

   Hint

   Focus on the definitions of reflexive vs irreflexive.

4. 4.

   True or False: A symmetric relation requires that both (a, b) and (b, a) are always present.

   • True
   • False

   Hint

   Consider the meaning of 'if'.

5. 5.

   Create a set A with 4 elements and define your own irreflexive relation. Show its matrix representation.

   Hint

   Remember no self-relating pairs.

6. 6.

   Can a relation both be symmetric and asymmetric? Justify your answer with a counter-example.

   Hint

   Analyze the definitions of each.