17.3.1. Definition and Characteristics

Try these first

1. 1.

   Define an irreflexive relation using set A = {1, 2, 3}.

   Hint

   Focus on pairs without self-relations.

2. 2.

   Give an example of a symmetric relation.

   Hint

   Ensure all connections are mutual.

3. 3.

   What is an irreflexive relation?

   • Elements must relate to themselves
   • No element relates to itself
   • Every element relates to another

   Hint

   Think about self-relations.

4. 4.

   If a relation is symmetric, what must be true?

   • True
   • False

   Hint

   Consider mutual relationships.

5. 5.

   Create a relation on set A = {1, 2, 3} that is both symmetric and antisymmetric but not reflexive.

   Hint

   Focus on self-relation conditions.

6. 6.

   Prove that the union of two transitive relations is also transitive.

   Hint

   Track connections across relations.