21.7. Implication of Equivalence Classes

Try these first

1. 1.

   What are the three properties that define an equivalence relation?

   Hint

   Remember the acronym RST.

2. 2.

   Give an example of a reflexive relation.

   Hint

   Think of numbers.

3. 3.

   Which of the following are properties of equivalence relations?

   • Reflexive
   • Transitive
   • Both A and B
   • None

   Hint

   RST is key!

4. 4.

   True or False: Equivalence classes can share elements with each other.

   • True
   • False

   Hint

   Think about the definition.

5. 5.

   Demonstrate how to prove that every equivalence class under a given relation is non-empty.

   Hint

   Start from the definition of an equivalence relation.

6. 6.

   Given that [0] and [3] represent two equivalence classes under modulo 3, prove whether they share elements or not.

   Hint

   Consider their definitions carefully.