18.7.1. Reflexive Closure

Try these first

1. 1.

   What does it mean for a relation to be reflexive?

   Hint

   Think about how elements relate to themselves.

2. 2.

   Given a set A = {1, 2, 3} and a relation R = {(1, 2)}, what pairs need to be added for it to be reflexive?

   Hint

   Self-referencing pairs are necessary.

3. 3.

   What is the reflexive closure of a relation?

   • A new relation excluding existing pairs
   • The smallest superset containing (a
   • a) pairs
   • A relation with no pairs

   Hint

   Think about examples of relations that include self-references.

4. 4.

   True or False: The reflexive closure can lead to the addition of duplicate pairs.

   • True
   • False

   Hint

   Remember the properties of union in set theory.

5. 5.

   Create a reflexive closure for the relation R = {(1, 2), (2, 3)} over the set A = {1, 2, 3}. What is the resulting relation?

   Hint

   Make sure to include all necessary self-references.

6. 6.

   In a network of friends, if R denotes relationships, how would you explain the reflexive closure in terms of social ties?

   Hint

   Consider self-identification in a social context.