22.4.2. From Partition to Equivalence Relation

Try these first

1. 1.

   Define a partition in your own words.

   Hint

   Focus on the key terms non-empty, disjoint, and covering.

2. 2.

   Give an example of a simple partition from everyday life.

   Hint

   Think of how people can be categorized based on shared attributes.

3. 3.

   What are the three properties of an equivalence relation?

   • Reflexive
   • Symmetric
   • Transitive
   • Only Reflexive
   • Non-empty
   • Overlapping-free

   Hint

   Revise the definitions of the properties.

4. 4.

   True or False: A partition can have subsets that overlap.

   • True
   • False

   Hint

   Consider what it means for subsets to be a partition.

5. 5.

   Given a set of students, partition them based on their grade levels and define the corresponding equivalence relation.

   Hint

   Consider how students in the same grade relate.

6. 6.

   Create a non-trivial partition of the set {1,2,3,4,5,6}, determine the equivalence relation, and verify that all properties hold.

   Hint

   Focus on pair combinations from each subset.