17.2.2. Examples of Symmetric Relations

Try these first

1. 1.

   Define a symmetric relation.

   Hint

   Think of how pairs relate to each other.

2. 2.

   Is an empty relation symmetric?

   Hint

   Consider the lack of pairs in the relation.

3. 3.

   What defines a symmetric relation?

   • Only (a
   • b) present
   • (b
   • a) must also be present
   • No pairs required

   Hint

   Recall the condition for symmetry.

4. 4.

   True or False: An empty relation is symmetric.

   • True
   • False

   Hint

   Think about lack of any relationship.

5. 5.

   Given the relation R = {(1, 2), (2, 3), (1, 3)}, determine if it is symmetric, and if not, why.

   Hint

   Look for missing reciprocal pairs.

6. 6.

   Create a symmetric relation with at least four pairs. Write out its matrix.

   Hint

   Ensure pairs maintain the symmetry condition while forming the matrix.