21.5. Question 4

Try these first

1. 1.

   What does it mean for a relation to be symmetric?

   Hint

   Think about mutual connections.

2. 2.

   Give an example of a reflexive relation.

   Hint

   Self-relationships are key.

3. 3.

   Which type of relation includes both (a, b) and (b, a) pairs?

   • Reflexive
   • Symmetric
   • Irreflexive

   Hint

   Think about bidirectional relationships.

4. 4.

   True or False: An irreflexive relation contains at least one pair (a, a).

   • True
   • False

   Hint

   Consider the definition of irreflexivity.

5. 5.

   Create a relation on set S = {1, 2, 3} that is reflexive but neither symmetric nor anti-symmetric.

   Hint

   Think of adding relationships that contradict those properties.

6. 6.

   Given a relation that is symmetric, can you prove it is also reflexive if it includes pairs like (a, a) for some a?

   Hint

   Visualize the elements involved.