1.1.5. Question 3: Counting Equivalence Relations

Try these first

1. 1.

   What is P(1)?

   Hint

   Think about how many ways you can group a single element.

2. 2.

   Is an equivalence relation reflexive? Yes or No?

   Hint

   Check if each element relates to itself.

3. 3.

   What does P(n) represent?

   • The number of elements in a set
   • The number of equivalence relations
   • The number of ways to arrange elements

   Hint

   Focus on equivalence definitions.

4. 4.

   True or False: An equivalence relation must be reflexive.

   • True
   • False

   Hint

   Recall the properties of relations.

5. 5.

   Given a set S with 4 elements, derive the formula for P(4) using the recurrence relation.

   Hint

   Think about adding the combinations of previous values.

6. 6.

   How does the nature of equivalence relations affect the size of a set?

   Hint

   Consider how partitions distribute elements across subsets.