22.3. Definition of a Partition of a Set

Try these first

1. 1.

   Define a partition using your own words.

   Hint

   Think about how you can divide a pizza without leaving any slices out.

2. 2.

   What is an equivalence relation?

   Hint

   Remember the properties that define this relation.

3. 3.

   What is a partition of a set?

   • A way of merging subsets
   • A collection of overlapping subsets
   • A collection of non-empty
   • disjoint subsets that cover the set.

   Hint

   Circle the option that emphasizes 'non-empty' and 'disjoint'.

4. 4.

   True or False: An empty subset can be included in a partition.

   • True
   • False

   Hint

   Remember the definition of a partition.

5. 5.

   Given the set S = {x | x is a positive integer less than 10}, identify all possible partitions of S.

   Hint

   Visualize different groupings without overlaps.

6. 6.

   Create a set with distinct integers and define an equivalence relation that results in at least three equivalence classes.

   Hint

   Think about how elements relate and group them accordingly.