18.6. Interpretation of Powers of Relation

Try these first

1. 1.

   What is the union of R = {(1, 2)} and S = {(2, 3)}?

   Hint

   Combine all pairs from both R and S.

2. 2.

   Identify whether the intersection of A = {(1, 2)} and B = {(2, 1)} is empty.

   Hint

   Look for common pairs between both sets.

3. 3.

   What does the union of two relations entail?

   • Combining all unique pairs from both sets.
   • Finding common pairs.
   • Determining relational paths.

   Hint

   Think about how you would gather pairs together.

4. 4.

   True or False: The composition of relations is commutative.

   • True
   • False

   Hint

   Consider examples of relation orders.

5. 5.

   Given a directed graph of 5 vertices with edges: {(1,2), (2,3), (3,4), (4,1)}, determine the transitive closure.

   Hint

   Keep tracking the paths through adjacent vertices.

6. 6.

   Construct an example of a relation that is reflexive and symmetric but not transitive.

   Hint

   Try building pairs while keeping those rules in mind.