18.5. Powers of a Relation

Try these first

1. 1.

   Define what a relation is in your own words.

   Hint

   Think about how pairs represent connections.

2. 2.

   What does the union of two relations represent?

   Hint

   Consider both conditions of membership.

3. 3.

   What does the union of two relations represent?

   • Only overlapping pairs
   • All unique pairs in both relations
   • Pairs from the first relation only

   Hint

   Think about combining two sets.

4. 4.

   True or False: The intersection of two completely disjoint relations is non-empty.

   • True
   • False

   Hint

   Consider what disjoint means.

5. 5.

   Determine the composition of the relations R = {(1, 2), (2, 3)} and S = {(3, 4), (4, 5)}. What is the resulting relation?

   Hint

   Follow the paths suggested by the relations.

6. 6.

   If you have a set of relations R = {(1, 2), (2, 3)} and need to form a symmetric closure, show your steps.

   Hint

   Remember to add the inverses of each pair.