22.3.1. Requirements for Partition

Try these first

1. 1.

   Define a partition in your own words.

   Hint

   Think of subsets that do not overlap.

2. 2.

   Give an example of two disjoint sets.

   Hint

   Look for sets with no shared elements.

3. 3.

   What is a requirement for a set to be partitioned?

   • All subsets contain the same elements
   • Each subset is empty
   • Each subset must be non-empty and disjoint

   Hint

   Think about the definitions we've covered.

4. 4.

   True or False: Two subsets can have common elements and still form a valid partition.

   • True
   • False

   Hint

   Remember the condition of disjoint subsets.

5. 5.

   Given the set {A, B, C, D, E, F}, create two different valid partitions and explain why they satisfy partition requirements.

   Hint

   Remember to check if all elements are covered.

6. 6.

   Can the equivalence classes generated from the relation of 'having the same first initial' on the set of names form a partition? Why or why not?

   Hint

   Think about names that would fall into the same equivalence class.