21.4.5. Part E: Reflexive and Symmetric Relations

Try these first

1. 1.

   Define a reflexive relation.

   Hint

   Think about pairs like (a, a).

2. 2.

   Give an example of a symmetric relation.

   Hint

   Consider relationships that involve mutuality.

3. 3.

   What defines a reflexive relation?

   • All elements relate to each other.
   • Each element relates to itself.
   • Only some elements relate.

   Hint

   Look for (a, a) pairs in the definition.

4. 4.

   Is the relation 'is taller than' symmetric?

   • True
   • False

   Hint

   Consider examples of height comparisons.

5. 5.

   Given a relation on set A = {x, y, z}, determine if the relation is reflexive, symmetric, or both.

   Hint

   Write down the elements and examine all conditions.

6. 6.

   Create a relation that is both reflexive and symmetric from a four-element set.

   Hint

   Start with the basics of reflexivity.