22.3.2. Trivial Partition

Try these first

1. 1.

   Define what a partition of a set is.

   Hint

   Focus on the key features of partitions.

2. 2.

   Give an example of a pairwise disjoint partition of the set {a, b, c}.

   Hint

   Make sure subsets do not share elements.

3. 3.

   What is a partition of a set?

   • A collection of overlapping subsets
   • A collection of disjoint subsets that covers the set
   • A single subset of the set

   Hint

   Consider how elements of the set are organized.

4. 4.

   True or False: The union of any two subsets in a partition can contain elements from outside the original set.

   • True
   • False

   Hint

   Think about what a set is composed of.

5. 5.

   Given a set of integers {1, 2, 3, 4, 5, 6}, list all possible partitions.

   Hint

   Consider how many ways groups can be formed without overlapping.

6. 6.

   Define an equivalence relation on the set of all students at a university based on their majors and describe the equivalence classes formed.

   Hint

   Think about how each class is related to the others.