17.1. Irreflexive Relation

Try these first

1. 1.

   Define an irreflexive relation in your own words.

   Hint

   Think about what self-relation means.

2. 2.

   True or False: An empty set can have an irreflexive relation.

   Hint

   Consider the contents of the empty set.

3. 3.

   What is an irreflexive relation?

   Hint

   Consider how elements relate to themselves.

4. 4.

   True or False: A set with one element can have an irreflexive relation.

   • True
   • False

   Hint

   Think about what happens in a one-element set.

5. 5.

   Create an irreflexive relation for the set A = {1, 2, 3, 4} and provide its matrix representation.

   Hint

   Include pairs that avoid self-referential elements.

6. 6.

   Explain why a relation on two elements cannot be both reflexive and irreflexive.

   Hint

   Consider each required pairing for reflexivity.