18.7. Closure of a Relation

Try these first

1. 1.

   Define closure of a relation.

   Hint

   Focus on the term 'smallest superset'.

2. 2.

   What does reflexive closure entail?

   Hint

   Remember, every element relates to itself.

3. 3.

   What is the reflexive closure of R = {(1, 2)}?

   • {(1
   • 2)
   • (1
   • 1)
   • (2
   • 2)}
   • {(1
   • 2)}
   • {(2
   • 2)}
   • None of the above

   Hint

   List the pairs that ensure reflexivity.

4. 4.

   True or False: A transitive closure may require multiple iterations to complete.

   • True
   • False

   Hint

   Think about what transitive means in relation.

5. 5.

   Given a relation R = {(1, 2), (2, 3), (3, 4)}, compute and explain its reflexive, symmetric, and transitive closures step-by-step.

   Hint

   Break down the steps, focusing on pairs added at each closure stage.

6. 6.

   How would you approach finding the transitive closure of a relation containing many elements? Describe your methodology and how you validate each pairing.

   Hint

   Consider writing pseudo-code to visualize your approach.