18.2. Intersection of Relations

Try these first

1. 1.

   Define union in the context of relations.

   Hint

   Think about combining all tuples.

2. 2.

   What is the intersection of two relations?

   Hint

   What is shared between both sets?

3. 3.

   What does the union of two relations give?

   • Common pairs only
   • All unique pairs
   • Only the larger relation

   Hint

   Think about including both sets' data.

4. 4.

   True or False: The intersection of two relations can produce a non-empty set.

   • True
   • False

   Hint

   What does shared mean in set terms?

5. 5.

   Given the relations R = {(1,2), (2,3), (3,4)} and S = {(2,3), (3,5)}, calculate R U S and R ∩ S.

   Hint

   Combine or find common elements based on their definitions.

6. 6.

   How does it demonstrate the properties of relations if you were to compose R and S and then find the reflexive closure?

   Hint

   Think of how composition tracks changes through paths, and closure ensures completeness.