18.7.2. Symmetric Closure

Try these first

1. 1.

   What is a symmetric relation?

   Hint

   Think about the definition of symmetry.

2. 2.

   If R = {(1, 2)}, is this symmetric? What would be its closure?

   Hint

   Check if you can find the inverse of the only pair.

3. 3.

   What is the purpose of symmetric closure?

   • To ensure pairs are reciprocated
   • To add arbitrary pairs
   • To narrow down the relation

   Hint

   Recall the definition of symmetry in relations.

4. 4.

   True or False: All relations are symmetric by default.

   • True
   • False

   Hint

   Think about the conditions that define symmetry.

5. 5.

   Given the relation R = {(1, 2), (2, 3)}, compute its symmetric closure and explain your steps.

   Hint

   List all pairs and their inverses systematically.

6. 6.

   Evaluate the necessity of minimal expansion in creating symmetric closures by discussing an example.

   Hint

   Consider how adding too many pairs can overcomplicate the relation.