18.1. Union of Relations

Try these first

1. 1.

   What is the union of two relations?

   Hint

   Think about all unique pairs.

2. 2.

   What does the intersection of two empty relations represent?

   Hint

   Consider what common elements exist.

3. 3.

   Which operation combines all unique pairs from two relations?

   • Union
   • Intersection
   • Difference

   Hint

   Think about gathering relationships.

4. 4.

   True or False: The intersection of two disjoint sets is empty.

   • True
   • False

   Hint

   Recall what disjoint means.

5. 5.

   Given three relations R₁ = {(1, 2), (2, 3)}, R₂ = {(2, 1), (3, 2)}, and R₃ = {(1, 3)}, compute the reflexive and symmetric closure of the combined relation.

   Hint

   Reflect on what pairs ensure reflexivity and symmetry.

6. 6.

   If a directed graph shows edges (1 to 2), (2 to 3) and (3 to 1), find the second power of the relation and describe its properties.

   Hint

   Track through the graph's paths as you consider powers.