22.6.1. Summary of the Lecture

Try these first

1. 1.

   Define an equivalence relation.

   Hint

   Think about how elements relate to each other.

2. 2.

   What is a partition of a set?

   Hint

   Remember what happens to the original set's elements in a partition.

3. 3.

   What is one property an equivalence relation must satisfy?

   • A. Only reflexive
   • B. Reflexive and transitive
   • C. Reflexive
   • symmetric
   • and transitive

   Hint

   Remember the three defining properties.

4. 4.

   True or False? Every equivalence class is empty.

   • True
   • False

   Hint

   Consider the definition of equivalence classes.

5. 5.

   Given a set of numbers S = {1, 2, 3, 4, 5}, define an equivalence relation that groups elements into three classes. Explain how your relation satisfies the three properties.

   Hint

   Describe the method you use to determine group membership.

6. 6.

   Construct a partition for the set of letters in the word 'HELLO' and relate it to an equivalence relation.

   Hint

   Think about how repeated elements influence group formation.